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An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?" Oops! You do not appear to have javascript enabled. We're making progress in getting things working without JavaScript. You may prefer to switch to Slashdot Classic for now. Re:Books (4, Insightful) I agree. I picked up the set a few years ago based on Surely You're Joking and I'd recommend them to anybody beginning in physics, especially to Professors of freshman physics, which is usually not so much taught as shoveled. The lectures are taken from his lessons in first year physics, so not too difficult for a math grad student with no previous physics. Re:Books (5, Informative) I just thought of another one. It's Mathematical Methods for Physicists by Arfken. I wouldn't necessarily recommend buying it, but find one you can flip through (most university libraries have it, as do most math/physics department libraries. and I can almost guarantee that someone you know has this book). Re:Books (3, Informative) I too cannot recommend "The Feynman Lectures on Physics Vol I-III" enough. This was written for first year undergrad students, but should have been aimed for 3rd year students. It is very nice in that is very detailed, at the expense of going overboard. For example, Feynman discusses the fact that solutions to differential equations are in fact the minimal energy solutions. I did not grok this until I got to grad school and studied Finite Element Methods. Another great series is the one by Laudau and Liftshitz. Re:Books (3, Interesting) As a 4th-year Physics undergrad, I have to voice my opinion that I absolutely can't stand Feynman's texts. They're nice to glance at, but approach the subject in a considerably different manner than any of the other renowned physics texts. Similarly, his proofs were terse to the point of being difficult to follow. I'll admit that my mathematical intuition isn't the greatest, though I can't help but think that this was intentional on Feynman's part, as to weed out those with weak mathematical skills from his freshman lectures. This makes them rather frustrating to use as a general reference. Similarly, the texts are largely theoretical, and offer little advice with regard to problem-solving. Personally, I've had good experiences with the Landau/Lifshitz series of texts, and it's hard to go wrong with Griffith's books on EM and QM. Goldstein's text on Classical Mechanics is also a well-known classic. That's not to say that that Feynman's texts are all bad. Some sections are outright brilliant, and he actually takes the time to explain himself rather extensively in many sections, which many physics (and math) writers frequently neglect to do. I keep a copy of all 3 volumes on my bookshelf, as they are occasionally handy. However, I wouldn't dream of using them as my only reference. Anonymous Coward \| more than 5 years ago Re:PDEs now? (5, Informative) You both probably studied how to solve certain simple PDEs in simple geometries (like the heat, wave, and Poisson equations). At a graduate level one normally learns how to prove existence and uniqueness of solutions to PDEs, how smooth those solutions are (i.e. how many derivatives do the solutions possess), and how to define weak forms of PDEs for which non-classical solutions exist (solutions that are not necessarily even continuous). Then there is the whole area of non-linear equations which is a very active research topic... (See the Navier-Stokes Equations.) Anonymous Coward \| more than 5 years ago Re:PDEs now? (5, Insightful) There can be a world of difference between graduate and undergraduate PDE courses; it's not like everything that's known about PDEs can be taught in a couple of undergraduate semesters. I expect most undergrad PDE courses are geared towards showing you the methods that work for a few classes of linear PDEs; a graduate course might be concerned with the analytical underpinning of those methods, or maybe about numerical and analytic techniques that are useful in solving classes of nonlinear PDEs, etc. That being said, though, from the way the original question is worded, it sounds like it's the first time this person has seriously encountered PDEs. Not having this happen until the third year of a PnD program does seem a little odd. Re:PDEs now? (2, Interesting) No. ODE's are typical of Undergrad. But, PDE's are typical of Masters. That isn't to say that PDE's are taught in Undergrad, period. Rather that PDE's in Undergrad is atypical. At least in North America. Other parts of the world either have vastly superior high-school/Undergrad or skip a lot of the, necessary for actually understanding, stuff. Germany and China are respective examples. Re:3rd year PhD student taking PDE? (1) I think his problems may be the result of how the questions are being given to them. They probably won't be your standard undergrad, here is an equation, give me the answer, type, but more of the here is the situation, figure out the equation, then solve it type. Halliday or Giancoli are nice (1) I've read through at least some of both Halliday and Giancoli, but sometimes it's nice to have someone explain things to you instead. I happened to have some very good physics professors who always explained where every equation came from (although sometimes I couldn't figure out what they were getting at until they said, "Trust me on this math here" and suddenly wrote equations on the board). Re:Halliday or Giancoli are nice (1) I don't recommend either Halliday/Resnick/Crane or Giancoli. They are both undergraduate texts treated at a rather simple level, light on math, and you'll never see a partial differential equation. That's the problem. Most texts that are basic physics also assume basic maths. Maybe you can handle Jackson Electrodynamics, which is a standard graduate level text. It won't be easy, but it doesn't really assume much foreknowledge, since it lays out the groundwork in the first few chapters (which are review for most students). Re:Halliday or Giancoli are nice (1) I dunno, I remember finally really "getting" pdes from H&R, though maybe that was very supplemented by lectures. I do know that as subjects go, what really made the math click was E&M: Maxwell's Equations were just so damn elegant and beautiful it all came together there for me (though coffee cups are good for boundary value problems - I seem to remember Boyce and DePrima being a good text with enough of the physics to make it work well). Partial differential equations (0, Offtopic) First of all, "partial differential equations (-1, Flamebait) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago First of all, "partial differential equations (4, Informative) Good thing you weren't modded up. Basically nothing you said was enlightening or even correct, except for the contents of the first sentence. You didn't even bother to correct the OP, you just sat back and decided to be a useless pedant. Yes, OP is technically incorrect, but your post is uninformative and completely worthless. All possible partial derivatives of a point on a 3-dimensional graph fall on a tangential plane. Usually we speak of a tangent line, setting x or y constant, but if one redefines the coordinates, then any line on that plane that passes through that point is a partial derivative. So that "partial derivative plane" contains all possible partial derivatives of that point. This designation is intuitive and not particularly misleading, so there was little point in being an ass about it. Anonymous Coward \| more than 5 years ago For EM and Quantum, even a math grad should read the advanced undergraduate books by Griffiths: Introduction to Electrodynamics Introduction to Quantum Mechanics For thermodynamics, I don't know the best text. For General Relativity, the standard undergrad book is Hartle's Gravity. But since you're a math PhD, you can go straight to the finest first grad level Relativity book by Sean Carroll: Spacetime and Geometry If you're looking for intuition, the indispensable and invaluable books are Feynman's Lectures on Physics. I can recommend mathematical physics texts, but I get the impression you want the missing background for understanding. Hope this is helpful. Re:Some essentials (4, Informative) I'd like to second all of these recommendations, but for Quantum Mechanics if your linear algebra is sharp, I might suggest Principles of Quantum Mechanics by Shankar. Griffifhs' Quantum Mechanics is an excellent introduction, but it assumes relatively little math knowledge, and tends to gloss over some of the assumptions being made. This is good for a student who's going to spend most of his effort trying to learn the practical aspects of doing Quantum Mechanical calculations, but not ideal for someone who grasps the math quickly and easily, and wants to really understand how things work. Shankar is a little more difficult mathematically (and is thus often a poor introduction for an undergrad) but it very clearly lays out the assumptions being made, and how the math relates to the physics. I haven't actually read the Sean Carroll book, but I took a course from him, and I can't imagine the book is anything but excellent. A survey of the best (3, Informative) Try Quantum Chemistry by McQuarrie for quantum theory--one of my favorites. It will get you up to speed on waves. I would have never thought there could be such a thing as a gentle introduction to the Schroedinger Equation, but McQuarrie is the closest there is. You can't go wrong with Atkins's Physical Chemistry for thermodynamics. For electrodynamics, there is Jackson. The classic on Information Theory is Cover and Thomas. For gravity, read Gravity (I've never read it though)--beware that its so thick, it has its own gravitational field. But I guess you don't mean relativistic physics. Decent Newtonian mechanics books are a dime a dozen because you don't need more than calculus to learn it. My favorites (2, Informative) I think the best book for what you are asking (and I am 95% sure this is the right book, but I've lent it out so I had to look it up from dover) is "Vector Analysis" by Homer E. Nowell. It develops the theory of vector calculus using an intuitive approach and builds up the theory of electromagnetism simultaneously. You might also look into the Feynman lectures. I do not normally recommend them as 'learning' material because, while excellent, I'm not aware that they come with any problem sets. But for you they may be a good supplement. And, just to throw it out there, but it seems to me that most technical schools have enough overlap between physics degree requirements and math degree requirements that if you have a reasonable interest in the other it might not be out of the question to work that into your curriculum. Man... (1) I'm in the exact opposite situation: I'm in a PDE class now with little grasp of the math but understand what they describe pretty well. I would hope you learn the material though, as I'd rather be able to get a solution from a mathematician. I don't know why you're snubbing undergrad books though - there are many that start to delve in the more advanced mathematics, enough so that it sets up the context for the PDEs. I'm a junior in nuclear engineering though - what's a 3rd year math PHD doing in PDE? Were you a Spanish major before?:) Re:Man... (1) for exceedingly strange definitions of "opposite," of course. if we are being that liberal with words, then, good sir, I, indeed, am in the exact opposite situation, and not you. I don't know anything about undergraduate level math or physics (well, perhaps this is also straining the definition for "undergraduate," given what is sometimes taught as undergraduate math in the US these days). Yes, stick to the mathematics. (2, Insightful) Seriously, the discussion of mathematical models in good PDE books is crisp and clear. The discussion in physics books is woolly and imprecise. That's because physicists rarely know enough mathematics to be able to express themselves precisely. So I would say: Just stick with the explanation of physical phenomena which you find in the mathematics books. It doesn't get much clearer than that, if you read the PDE books which I used to read. Pick a different curriculum, seriously (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago If you're uncomfortable with PDE without Physics, then your curriculum is probably Mathematics and if you can't handle PDE, change majors, seriously. A Mathematics degree alone requires theoretical and abstract thinking to be successful. Seriously, find a Math counselor and talk to them about it. You'll never find any quick tutorial on Physics, unless of course you're Einstein or Newton. Wave phenomena are complicated to begin with.... (1) Having taken PDE's last year as a Nuke-E undergrad for intro to quantum, I can tell you that all the physical phenomena PDE's model are generally 'wave' based in _concept_. I also took our Physics 340 on "Heat Waves and Light" which is most of the stuff relevant to PDE's.... The textbook for that course was "Selected Chapters from 'University Physics', Young and Freedman, 11th edition." Where selected chapters were all the ones dealing with heat, waves, light, and a teeny bit of relativity. It's a pretty standard university physics textbook. Anonymous Coward \| more than 5 years ago Re:What? (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago There's a huge difference between the intro PDE class that undergrads usually take - and the more advanced ones that graduate students take. My concern is that he's a third year grad student...and is asking questions like this on slashdot when he should already know the answer. Re:What? (4, Informative) Contrary to what most people seem to think, the material taught in most Calculus and Differential Equations courses has very little resemblance to what most Mathematicians study. These fields actually all fall under the heading of Analysis, which is just one of several major branches of mathematics. A student not interested in analysis could easily spend most of his math career working in another area. For the most part, differential equations courses are aimed at non math majors, such as physicists, chemists, engineers, and the more analytically minded biologists and economists, so even a Math major specifically interested in analysis isn't necessarily going to take classes on partial differential equations. I myself double majored in Physics and Math, and every single course i took about differential equations was for the Physics major rather than the math Major, so I think that Math grad student could quite easily end up with a PhD without ever dealing with differential equations unless they interested him. Re:What? (3, Insightful) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago Wow, the level of ignorance here is astounding, that you would get moderated so highly. Real PDE (as mathematicians study it) is HARD, and requires a heavy background in analysis. This is not the same as undergrad "PDE" courses. This is like the high schooler saying "Why are you taking algebra as an undergrad" to a math major studying abstract algebra. Its the same word and the topics are related, but its not even close to the same thing. Re:Some recommendations from another Math Ph.D (1) The OP is a graduate student in a field that isn't physics and says he never took physics anywhere. He's overestimating his abilities when he says he doesn't want to start with an undergraduate textbook because that's exactly where he should start. Unless he's cramming for an exam, he should take the time to start with college physics books and move up as he understands the material. PDE is difficult, but the basic physical concepts they represent are relatively simple to understand. Jumping Jesus on a pogo stick, you're pointing him to The Black Death straight out of the gate? Why not give him underwear made of wolverine chow? Wheeler would have died ten years ago if not for the life-giving tears of those who opened that book unprepared. That is to say, everyone. Seriously, dial it back a bit. First, hit the Feynman lectures (stop when you get to 'partons'.) Then, for someone coming from a mathematical bent, I'd suggest starting with Sokolnikoff's book "Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua", which covers a lot of ground besides GR. Due to the absence of a just and loving god it is out of print, but surely one of the profs in a math department with a PhD program has a copy (or at minimum the library.) And there's always copies on Alibris. And, seconding suggestions from other posters, Kittel and Kroemer's "Thermal Physics" is a good starting point on thermo, As for quantum, in the absence of all knowledge in the field I'd start with Tipler's "Modern Physics", with the goal of ramping up to Cohen-Tannoudji, Diu, and Laloe's "Quantum Mechanics".The material he is describing is what is covered in the undergrad PDE course. Its frequently given as both an undergrad course number and a graduate course number: same book, just more work for the grad level class. not bitter (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago Not to sound bitter or anything, but you took a Ph.D. spot that a qualified student was rejected for. The fact that you are even asking the question you asked, means you are nowhere near where you should be for entry into a Math Ph.D. program. It's a serious deficiency. not only to just be getting to PDE's, but to never have studied physics. How did you get a math undergrad without physics, and at what institution? Physics/Astronomy Graduate student perspective (3, Informative) Off the top of my head I would say... Introduction to Partial Differential Equations Applications - E. C. Zachmanoglou & Thoe; mostly math already, but has applications. For introduction to the wave equation try The Physics of Vibrations and Waves - Pain. The Shrodinger equation is explained well in Quantum Mechanics - Griffiths. Road to reality (4, Informative) An excellent Physics book that is very math heavy but assumes no prereqs is Penrose's Road to Reality. This pretty much covers all of the main theory/formulas in cosmology, and he has 350 pages of math (much of it graduate level) to get there. The Feynman Lectures on Physics (4, Informative) I can not recommend these books enough. Feynman does a brilliant job of bringing the concepts of physics to life. All together, they are quite extensive, but the individual topics are brief enough to digest in one sitting. Wether you only have a passing interest in physics, or a graduate degree in the field, you will find that there is much to appreciate in these lectures. Even for those simply taking physics as requirement, I think that these would give you a real appreciation of the field, and probably make the classes a lot easier at that. They're All Targeted for Mathematicians (5, Informative) I've a couple of degrees in Physics, and I assure you, half the print in the _vast_ majority of Physics books is equations. Most physics texts seem to assume a math minor. Most Physics majors first see partial differential equations, special functions, and group theory as undergraduates. A couple of friends took partial diffeq for fun. Yeah, that's one way to know you're a nerd. I suggest a library or a used bookstore, as these things are expensive. Here are some of the typical texts you see around on various physics topics (by author's name, because the titles are useless): Electromagnetism: Griffiths is a really great undergrad book, which is easy to read. Jackson is the classic first semester grad-school book. Math Methods of Physics: Arfken is a classic. Cantrell is an up and coming variant. Thermodynamics: Kittel is an oldie, but a goodie. Someone else prolly has a better suggestion. General Undergrad Phenomonology: The World Wide Web - Invented at CERN, y'know. Halliday & Resnic is probably the easiest book to find. Serway is newer. Relativity: Rindler is the standard. Mechanics: Goldstein is pretty easy to find. Quantum: Landau (yep, the same) and Lifshitz is a solid text that hits on Shcrodinger's equation well. Griffiths is easier to read, as is Eisberg & Resnick. Modern Physics: Less of an obvious choice, but it'll be a good source for more sexy topics. A lot of partial diffeq is used in mechanics. IIRC, partial diffeq was invented to describe mechanical systems, so many of the examples are very intuitive (for you of course, not for 99.9% of the population.) i DO recommend an undergrad physics book... (1) as a recently graduated engineering student, and having taken my share of advanced calc and physics, i would actually recommend an undergrad physics book geared towards engineers. this is probably the best place to start in understanding how the equations you mentioned apply... Don't be an ass. Oops, sorry, too late... (2, Informative) A 4- or 6-year degree in math or science should include both math and science. If not, you are NOT receiving the education you need to really understand your field. Regardless of how you feel, mathematics actually relates to (and is constrained by) our physical universe. If you do not understand that, then you are not well versed in either. A degree in mathematics, from a responsible university, should include at least some physics. And of course a degree in physics requires a certain minimum of math, or you will not understand the subject. What I was getting at is that it actually does work both ways. An understanding of our real world (physics), often constrains what real mathematicians do once they leave the university. You will not make it very far as an actuary, for example, if you do not understand at least the basic physics of what happens when someone experiences an automobile crash or a myocardial infarction. Psychology adds to a broad education, but that is not even remotely related to what I was saying. Nor philosophy, nor accounting. I was not suggesting a educational free-for-all, just that physics and mathematics often go hand-in-hand. I would not require it, but I do believe that it would benefit most people if they did have at least a little of each. I have. More than a little, actually. But all that aside: math and physics are closely related "hard sciences". Philosophy, psychology, and accounting (we might as well include sociology and art history here), are all valuable education (at least I think they are), but they are NOT hard sciences, nor are they related to the subject at hand. In future, please stick to the matter under discussion. a few suggestions... (1) Since you want intuition, an introductory undergrad book might actually be a good idea. Higher level books will often assume you have seen the subject before. Quantum Chemistry by McQuarrie is a good first book for quantum mechanics and the Schrodinger equation. Dirac's book is more advanced but also good (much harder to read). Much different focus though. For electricity and magnetism a good first book is Griffiths Introduction to Electrodynamics. Here you'll see applications of the Poisson and Wave equations. Jackson is the classical "second" course textbook. (Upper level undergrad, beginning grad). A good introduction to applications of the diffusion (i.e. heat) equation is Random Walks in Biology by Howard Berg. One benefit is that it is a very short book too! For nonlinear equations there are too many references to know where to begin... There are millions of books on just the Navier-Stokes equations... Generally I'd just poke around Amazon and browse some of the books with good reviews. Anyways if the original poster wants references for a specific PDE or area of physics please post a followup... Mathematical Methods for Engineers and Scientists (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago There are three of them is the series and it is a little pricy but I have never seen anything explained this well. The author K.T. Tang has a constant named after him, an equation and an office at the Max Plank institute. He teaches at a small liberal arts school in tacoma, washington. I don't know why. But I was lucky enough to be given print offs of the book, for his class, before it was published. Not to bring you down or anything, but.... (0, Flamebait) I have not yet finished college.. forced to take night classes, and have no where near as much campus time/experience as you and many others have, but it only took me about... oh, 20 seconds to Google for some good sites, and has links to pretty much all you mentioned. The links there point to other links for further reading. Note that in the reference section of wikipedia articles are links or information to books and such. I believe they're called citations. (citation needed) As a third-year PhD math student..... I'd think you would already have tried Google or Wikipedia. Your browser should have them on speed dial. So, really, what is your question? Re:Not to bring you down or anything, but.... (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago Do you have any idea how many books there are out there? We need guidance from people in the know as to which ones are the most suitable for us. This person's question was legitimate. Googling `Partial Differential Equations' is not the answer. I'm sorry but, WHAT? (1) What do you mean you are a third year PHD candidate in mathematics and you are only now taking PDE!? I took that sophomore year in my undergraduate engineering program, before we got into any of the serious engineering classes. If I remember correctly, it was the same time as we studied relativity in physics. What have you been doing all this time... Vector Analysis (2, Insightful) is where to start when it comes to deriving PDEs. The heat equation and the wave equation fall easily out of vector analysis, as do a number of other familiar PDEs. I'd start with a vector analysis book. 3rd year Math PHD and only NOW learnin Partial Dif (1) My god, I had to learn that crap as a freshman UNDERGRAD!!! Now grant it I was an electrical/computer engineering major at the time, but still, I can't believe that a third year math PHD candidate would not have had partial diffs... I mean, seriously, it is the only way to do some stuff, especially anything in the real world (hence all the physics basis on the questions). Re:3rd year Math PHD and only NOW learnin Partial (1) The difference between engineering and math is that engineering focusses on real-world problems and the bit of math required to solve them. Because there are too many other things to learn - and engineering centers on practical applications. A lot of math appears to be intellectual masturbation unless you have proper training - and lacks any trivial practical application. Until suddenly, someone might find use for it to describe something in physics. Or not. A lot of the riddles you solve as a geek are applied math. Think topology. Why would an engineer have to bother with abstract algebra? Or why should he be able to derive about everything in math from aimple set of axioms?:) Engineers don't know math. Much. (Disclaimer: Here speaks a CS guy who used to date a lovely Math PHD. And I thought MY mind was warped...) Anonymous Coward \| more than 5 years ago Another good supplement is The Variational Principles of Mechanics by Cornelius Lanczos of functional analysis fame ( However, you will also want something on thermal physics and I have no awesome suggestions for that. But in classical mechanics you should get a lot of nice PDEs (such as the wave equation) which will be covered by the sources I mention. In electrodynamics you will get Laplace's equation (which will also show up in gravitation in classical mechanics). There are no really good books on QM that have been published, so I would just not worry about getting the physics behind the SchrÃdinger equation. thermodynamics (1) The wave equation and diffusion equation are technically partial differential equations because of the 3 space dimensions and time, but these are simple PDEs because the three space dimensions are basically the same and the derivatives usually only appear as the Del operator, which treats each direction equally, and the boundary conditions are usually such that the constant of integration is just zero. In thermodynamics, you actually have serious PDEs which involve variables that aren't all the same, and the constant of integration must be found by matching arbitrary functions to each other and boundary conditions. This probably isn't a book for someone new to physics, but it does use some PDEs. Good PDE book with relations to Physics (1) I am currently taking a pde course as an undergrad and am using Partial Differential Equations: An Introduction by Walter A. Strauss. While this book does have some faults it does an excellent job of relating pdes to their physical interpretation. To all the people suggesting Griffiths QM.... (0) This comment was hidden based on your threshold setting. Anonymous Coward \| more than 5 years ago That book is terrible. He should have stopped after his masterpiece on Electrodynamics. Griffiths will simply not have enough math. To reiterate, Griffiths Quantum Mechanics book is bad, his Electrodynamics book is genius. road to reality (1) I can recommend "The road to reality - a complete guide to the laws of the universe" by Roger Penrose. The guy undoubtedly knows what he's talking about (being a famous physician himself) and the book is very math-centric. First the mathematical concepts are explained, then based on that the physics of our universe. Anonymous Coward \| more than 5 years ago learning by applying (1) I hope some math professors are reading this. They always seemed to think that they only needed to teach the "how", as "why" would already be obvious or would become clear. It didn't, not for me. More like that was the excuse, because actually "how" alone was much easier to teach. I studied PDEs in calculus classes, but never used them for anything. When they did come up with example uses, they were pretty contrived, and often could be solved with plain old algebra. Or they were so small that hand application of numerical methods could pin down the answer. Took only a few iterations of the Bisection method to get that zero, or you'd hack up a quick and dirty program to push some data into a linear algebra library function and get back results, something like that. And what's a student to think on hearing that although faster, Newton's Method, which is based on calculus, isn't as reliable as Bisection, which is simple algebra. Not good examples when trying to show students how useful and valuable calculus is. Books? There's more than books alone out there. Lots of material on the web. Lots of combined material. Here are some books associated with Sage. Are you making use of mathematical software: Sage, Matlab, Mathematica, Maple, or some such? Or are you at least able to code up something in a general purpose language if needed? Much math is to the point where you can't advance without computers. Maybe I'm a bit behind. These days, I suppose all math students use such software. I've noticed also that people with backgrounds in pure math don't have a good basic understanding of Computer Science. You know all about Fourier Transforms, you've heard of the Fast Fourier Transform, you've heard of big O, but you don't see what the big deal is about the FFT-- to you FFT is just one of many ways to do a Fourier Transform, one specific to computers which a person would not use if working out such a transform on paper. Do you have an appreciation of the algorithmic complexities of the math problems you are encountering? The way multiplication is done in grade school is just fine for relatively few small numbers, but when you want to do millions of multiplications of large numbers (1000 digits, say), you'd better use a computer, and you'd better program the computer to use FFT. A textbook on Numerical Methods could be worth checking out. E&M (0) Anonymous Coward \| more than 5 years ago If you're curious about E&M, I suggest you look at Purcell's "Electricity and Magnetism". The book starts at a basic level (physics-wise, not math-wise) and works its way up. You start with monopoles, derive the field from the inverse square law, move onto lines and sheets of charge, then dipoles, voltage & current, electronic circuits (resistors, capacitors, inductors, DC, AC, calculating V and I with diff eq, etc.). Then you combine special relativity with the electric field and get...magnetism! Next you go through dipoles, electromagnetic radiation, induction, derive Maxwell's equations from scratch, and learn about how E&M fields interact with matter at the atomic through macroscopic scales. The problems aren't your standard "Find X given Y using equation 5" problems. These actually make you think. Some examples off the top of my head: -Find a resistor equivalent to an infinite repeating pattern of small resistors -Prove that no magnetic field surrounds a torroidal electromagnet using Gauss's law -Calculate the capacitance of two concentric hollow spheres 500 pages of physics and math. If you can understand half of it, you'll be well grounded. (No pun intended.)
What types of math are used a lot when developing games? Hello! I will be starting college in a few weeks and I am majoring in Computer Science. I know that in order to complete my degree I will have to learn all sorts of math, but I was wondering what types of math are use a lot when developing games. It depends a lot on the type of game you're making, as well as your role in the production, as well as what kind of tools you're working with. If you're working with a good framework, you won't strictly speaking need to understand the math as well as if you're making your own stuff. That said, you do have to know when to apply the various functions you might have available to you. Keep that in mind -- extensive knowledge of all of the following might be somewhat daunting. The more you know, though, the better you can apply the math to solve all kinds of things. Linear algebra, trigonometry and vectors will be important in a lot of different areas. Various statistics and probability can come in handy for different things, including balancing gameplay. For 3D programming, you can expect to run into vector math even more -- dot and cross products, normals, etc. Trigonometry even more, including polar coordinates. Various math related to geometric shapes -- plane, ray and sphere equations. Depending on what kind of frameworks you'll be using, some knowledge of matrix math will be useful. For physics related things you might have to learn some physics (at least some formulas), e.g. ballistic trajectories. Calculus stuff. You'll want to be comfortable with converting between radians and degrees. --- There's probably a lot of areas I've missed, but I remember there being a similar post a while back. I'll go look for it. For working with 3D graphics Matrices are what you'll most likely be working with as they make complex problems relatively simple and are very powerful. Understanding trigonometry both in 3D and 2D space is quite helpful as well. Depending on what you are doing in your game you can scale through lots of levels of math, but just remember you don't have to be a genius in math to program them. Formulas already exist and I think it's more important to know how to look at a concept or loose formula and implement it. Knowing the math makes it easier, but without doesn't make it impossible. 80% of game development by volume is basic algebra -- relatively simple expressions with a few constants and variables, sprinkled with basic operators (+, -, *, /, pow, sqrt). High school level stuff. The other 20% by volume is comprised mostly of linear algebra, trigonometry, geometry, calculus, and statistics--roughly in that order in my experience--but the particular mix tends to vary depending on what your focus is. However, this 20% by volume accounts for a much higher percentage by utility and by difficulty. Its the stuff that makes things work elegantly or work at all. The more knowledge you have in these areas the better, but you can accomplish a great deal with just a solid understanding of the fundamentals--knowing more in these topics tends to let you see better solutions and make optimizations, but doesn't tend to be fundamentally limiting if you don't know more than the basics unless you have a very specialized focus. Then, there are other mathematical topics that you might not apply directly, but which help you understand your systems better -- things like discreet math, algorithm analysis, and big-O notation. These are things that help you understand correctness and performance at a higher level, they give you the tools to make educated guesses about which of many potential approaches are better without having to implement and evaluate them. They also give you the tools to understand the root of a problem based on its mathematical symptoms -- things like numerical instability of floating point numbers under certain conditions, or performance regressions that result from new algorithms. Knowledge in vectors and matrices is a must. You may get away without a broad knowledge in matrices though. But more advanced features will need more mathematics. Linear algebra in general and calculus to some extent are very common. The moderators don't generally frown on duplicated content unless the topic is seriously over-served. Besides, The linked thread specifies 3D games, while this one doesn't specify -- there's a lot of overlap but the differences are not vanishingly small. But I do agree that the linked thread has a lot of good discussion. Its worth reading. As others pointed out, linear algebra is used daily. Linear algebra is the math that covers 3D manipulation. It includes matrix manipulations, vectors and their manipulation, and most simple spatial manipulations. Large portions of linear algebra is extension of the 2D manipulation of trigonometry, so you need to know trig as a prerequisite. Of course this also includes lesser math like algebra in order to actually do the math, so all of that is incorporated by reference. Statistics has probably been my second most frequently used math. Coming up with permutations is common, as is ensuring things happen according to adjustable frequencies. Usually this isn't too hard, simple multiplication or data set manipulation, but you do need to understand the basics. Calculus is used infrequently unless you are working on physics engines. Most people aren't working on physics engines, so you probably won't NEED it.. It is nice to have on occasion, but if you have the above skills you can usually get by without it. Discrete mathematics is useful if you take it. All computing is discrete mathematics, there is no infinite precision inside the box. Number theory can be useful to understand, but isn't really necessary. There are college courses on fluid dynamics that some people might find useful. Topology coursework might be useful to you, since most 3D models are representations of surfaces and topologies. Business mathematics can be useful if you want to go into the business side of games. There are many business-oriented math topics, such as business calculus and business statistics, both focusing more on how to apply the math in a business environment. From all of that, I recommend college algebra, a year of college calculus, college stats, and a year of college linear algebra. More if you have time in your schedule and if you have an interest in any topic. I have heard many people complain about not having enough math background. I have never heard anyone seriously complain about knowing too much math. (I heard a few people joke about it because people were always coming to them to help with math problems in their code.) Computer science in many ways is applied mathematics. It is difficult to have too much knowledge.
Introduction: This course is a way for you to acquire or review some basic mathematical skills that are essential to any further work in math or science. Goals: You will learn how to manipulate algebraic expressions. You will learn how solve equations and inequalities. You will learn the basics of functions. You will learn some properties and applications of polynomial, exponential, and logarithmic functions. You will learn how to graph these functions. What is required of the student? As with most endeavors, what you get out of this course will be directly related to what you put in. Mathematics can not be learned just by watching. You have to actually do the mathematics to learn it. A great deal of the class time will be spent with students actually working problems at the board. I am always happy to answer questions during class or in my office. Grades: Grades will be determined on a 1000 point scale as follows: 4 Tests @100 each for 400 points Final Exam 333 points The other 267 points (or more) can be collected as described below. On the 1000 point scale this is how the letter grades are determined: 900-1000 A 800-899 B 700-799 C 600-699 D 0-599 F Accumulating points: Almost every class period you will have a chance to work problems on the board. You can obtain 3 to 7 points if you work one of the problems from the textbook. I will both call on students and ask for volunteers. You should come to every class prepared to work problems. The problems from the textbook that I will ask you to do at the board will be selected from the list found at math1111problemlist.pdf or will be problems of my own that I will come up with during the course of the semester I will give you an idea which problems you might be called on to work the class period before. If you have a question about a specific problem and want to see it worked, I will ask someone to work it on a volunteer basis. The volunteer will receive 8 to 10 point for this type of contribution.Finally you can earn points by doing the online homework that comes as part of the MyMathLab software that accompanies the custom textbook. For each homework assignment completed with an 80% or better score you will earn 7 points. I reserve the right to give you other opportunities to earn points as well. Note that points are never taken away from you for any contribution that you make, so you should take every opportunity to earn points. For more information on getting started with MyMathLab go to StudentRegistrationHandoutfor1111F13.pdf. Attendance: Attendance is expected at all class meetings. If you miss more than 3 class periods I will withdraw you from my class. If I withdraw you before midterm you will receive a W. If I withdraw you after midterm you will receive a WF. You are responsible for any work that you missed during an absence. Please come see me as soon as possible if you have missed a class or if you need to miss a future class. You will also lose the opportunity to collect points by missing class. Withdrawal: The deadline for withdrawal with a grade of W is Monday October 14, 2013. Any withdrawal after that date will result in a WF. If you feel that you must withdraw please try to do so on or before October 14. Make-up policy: No in-class work can be made up. A make-up test may be given if an extreme situation makes it impossible for you to be there for the test. Examples of extreme situations include illnesses, accidents, or family emergencies. You must let me know as soon as you find out that you cannot make it to the test. In almost all cases this means that you will let me know before the time the test is scheduled. You must be willing to provide written evidence of the particular situation that requires you to miss the test. No make-up final will be given. If an extreme hardship requires you to miss the final exam you will receive a letter grade of I (incomplete). The "I" can only be changed to a passing letter grade by taking the final exam at the beginning of the following semester or taking the course over.
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(CTE) MATHEMATICS IN COMPUTER AIDED DRAFTING Math IV Unit Pacing Guide Rational and Purpose: Professional math IV is provided to enhance mathematics in high school and provide students with the math skills necessary for the current job market and/or prepare students for college entry. Curriculum that is contained within Career Technology Education (CTE) provides enhanced mathematics instruction that makes mathematics more explicit in a meaningful context and helps reinforce students' mathematics understanding both in and out of context. Guidelines: All objectives must be mastered at or above a 70% efficiency level in order to receive 1 Math credit. The content/objectives to be completed in four (4) semesters are listed below in each trade specific program. Since each program contains differing content at various stages, an independent content/objective list will be constructed for each curriculum in every course. 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Addition and 1st quarter 1 After comp leting this unit the MA1, Whole numbers Worksheets of Paper and pencil Test of at least 10 subtraction of week Student will be able to calculate Real numbers addition and problems and problems in each whole nu mbers whole nu mbers through the Goals: Natural nu mbers subtraction software operation to mathematical processes of addition, G, 1.10 Nu mbers problems demonstrational demonstrate subtraction, Addend, Sum activities mastery CLEs N-1B, Minuend N-1C. M -2D Subtrahend DifferenceMultiplication 1st quarter 1 After comp leting this unit the MA1, Whole numbers Worksheets of Paper and pencil Test of at least 10 and division of week Student will be able to calculate Real numbers mu ltip licat ion and problems and problems in each whole nu mbers whole nu mbers through the Goals: Natural nu mbers division problems software operation to mathematical processes of G, 1.10 Rational demonstrational demonstrate mu ltip licat ion numbers, activities mastery and division. CLEs N-1B, Multiplicand N-1C. M -2D Multiplier Product factor, Quotient divisor, Div idend Reducing proper 1st quarter 1 After comp leting this unit the MA1 Prime nu mbers Hardcopy Paper and pencil Test of at least 10 and improper week student will be able to add & Greatest worksheets, video, problems and problems in each fractions subtract proper and imp roper Goals: common factor, internet and other software operation to fractions G, 3.3, 3.4 Least common electronic sources demonstrational demonstrate mu ltip le, activities. Peer mastery CLEs Rational grouping for N-1B, N- 1C, expression, additional support N-2D, N-3E Nu merator and interaction. Denominator Recip rocal Equivalent Add fractions 1st quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers Hardcopy Paper and pencil Test of at least 10 With like week student will be able to add rat ional Greatest worksheets, video, problems and problems in each denominators numbers with like denominators Goals: common factor, internet and other software operation to and reducing to and reduce them to lowest terms G 1.6, 1.10, Least common electronic sources demonstrational demonstrate lowest terms 3.4 mu ltip le, activities. Peer mastery Rational grouping for CLEs N-1B, expression, additional support N-1C,N- Nu merator and interaction 2D,N- 3D, Denominator Recip rocal Equivalent Add fractions 1st quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers Hardcopy Paper and pencil Test of at least 10 with unlike week student will be able to add rat ional Greatest worksheets, video, problems and problems in each denominators numbers with unlike denominators Goals: common factor, internet and other software operation to G 3.3, 1.6, 3.4 Least common electronic sources demonstrational demonstratemu ltip le, activities. Peer mastery CLEs Rational grouping for N-1C, N-2D, expression, additional support N-3D, N-3E Nu merator and interaction Denominator Recip rocal Equivalent Add fractions 1st quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 With unlike week student will be able to add rat ional Greatest worksheets, video, problems and problems in each denominators numbers with unlike denominators Goals: common factor, internet and other software operation to When neither is when neither is lowest. G 3.3, 1.6, Least common electronic sources demonstrational demonstrate lowest common 1.10, 3.4 mu ltip le, activities. Peer mastery denominator Rational grouping for CLEs N-1B, expression, additional support N-1C, N-2D, Nu merator and interaction N-3D, N-3E Denominator Reclike numbers with like denominators. Goals: common factor, internet and other software operation to denominatorsunlike numbers with rational nu mbers Goals: common factor, internet and other software operation to denominators when neither rational number has a G 1.6, 1.10, Least common electronic sources demonstrational demonstrate common denominator. 3.4 mu ltip le, activities. Peer mastery Rational grouping for CLEs N-1B, expression, additional support N-1C,N- 2D, Nu merator and interaction N- 3D Denominatorlike rational nu mbers with likeunlike rational nu mbers with unlikemixed numbers week student will be able to subtract Greatest worksheets, video, problems and problems in each and reducing mixed numbers and reduce their Goals: common factor, internet and other software operation to answers to answers to lowest terms. G 1.6, 1.10, Least common electronic sources demonstrational demonstrate lowest terms 3fractions when week student will be able to subtract Greatest worksheets, video, problems and problems in each borrowing is rational nu mbers when borrowing Goals: common factor, internet and other software operationnecessary is necessaryMultiplying 2nd quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 fractions week student will be able to mu ltip lyMultiplying 2nd quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 fractions and week student will be able to mu ltip ly Greatest worksheets, video, problems and problems in each whole nu mbers rational nu mbers and whole Goals: common factor, internet and other software operation to numbersDiv iding 2nd quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 fractions week student will be able to d ivide1C,N- 2D, N- Denominator 3D, Recip rocal Equivalent Changing 2nd quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 common weeks student will be able to Change Greatest worksheets, video, problems and problems in each fractions to common fractions to decimal Goals: common factor, internet and other software operation to decimal fract ions fractions and decimal fractions to G 3.3, 1.6, Least common electronic sources demonstrational demonstrate and decimal common fractions. 1.10, 3.4 mu ltip le, activities. Peer mastery fractions to Rational grouping for common CLEs expression, additional support fractions N-1B, N-1C, Nu merator and interaction M-2D, M -3D, Denominator M-3E Recip rocal Equivalent Addition, 2nd t quarter 1 After comp leting this unit the MA 1, MA 5 Prime nu mbers, Hardcopy Paper and pencil Test of at least 10 subtraction, week student will be able to add, subtract, Greatest worksheets, video, problems and problems in each mu ltip licat ion mu ltip ly and divide decimal Goals: common factor, internet and other software operation to and divisions of fractions. G 3.3, 1.6, Least common electronic sources demonstrational demonstrate decimals to 1.10, 3.4 mu ltip le, activities. Peer mastery recognize and Rational grouping for collect data fro m CLEs N-1B, expression, additional support Tables and N-1C, M -2D, Nu merator and interaction Charts and use M-3D, M -3E Denominator this data to Recip rocal perform mo re Equivalent advanced Calculations I Measurements, Conversions, Rotation of Angles, and Trigonometry Ratios of Acute and General Angles Core Concepts: Students will learn: How to accurately interpret different measurements using different scales and units of measure; Differentiate between standard English and Metric conversions; Assess different directions and rotations of angles in reference to the unit circle; and discover the relationships between acute and general angles. Comp. # 1 3rd quarter 2 After comp leting this unit the MA 1, MA 2, Architect Rule Div iders/compass Classroom Students will be weeks student will know all fract ion and MA 4, MA 5 Angles Protractors demonstration of given a 50 Be able to decimal incremental equivalents on Degrees Rulers how to use various question test measuring devices accurately an exploded view o f an inch; Goals: (Fractional Meter sticks involving the interpret understand and identify all rat ios, G 1.6, 1.10, Degree) Yard sticks Lecture on how to recognition of different units of scales, actual size, and smallest 2.7 Nu merator Angle finder interpret various fraction to measure using calibrat ions found on an architect Denominator Architect Rule scales and units of decimal different scale rule; be able to measure with any of CLEs Vertex Elmo measure using an conversions, measuring the 12 d ifferent scales on an N-3D, N-3E, Side Projector Elmo Zoom decimal to devices. architect rule : G 4B, M -2Dc (Center Mark) overhead projector fraction (Architect Scale) Unit Circle conversions, fill Units of Measure The students will be in ratios when given guided Smallest given a scale, and practice on how to Calibrat ion complete a table of fill in scale when Ratios all ratios, scales, given a ratio. Scales actual size, and smallest calibrations There will be a found on an written test on architect rule. measuring and accuracy. The students will complete an extensive assignment on scale interpretation and actual measuring practices C&I-PacingGuide-Unit-05/08 (Content within Pacing Guide Produced by: David W. Hall) Learn ing Show-Me Activities & Time Span Standards and Instructional Co mpetencies (quarter/wks) Course Objectives CLE Code Vocabulary Resources Strategies Assessment Comp. # 2 3rd quarter 1 After comp leting this unit the MA 1, MA 2, English system Access to an on- On-line . week student will be able to co mpare MA 5 Metric system line co mputer conversion The students will Differentiate equivalent measurement units and Equivalent source programs be asked to between conversions to interpret proper Goals: Meter measure several Standard English dimensioning. G-1.10, 1.7, Decimeter Paper and pencils Short lecture objects using a and Metric 3.4. Centimeter using and standard and conversions Millimeter Chart of metric explaining the metric measuring CLEs Kilo meter conversions metric system device to N-1C, M -2D Feet formulate their Inches Worksheets Review of how to own conversion Yard which contain find and calculate factor conversion a conversion problems factor. They will then be given a written Chart of Metric- Worksheets test Customary handed out for Equivalents guided practice Comp. # 3 3rd quarter 2 After comp leting this unit the MA-1, MA-2, Trigonometry Handouts of Class will watch a There will be a weeks student will understand angles and MA-4 Angles Trigonometry video lesson written test to Assess different angle measurements, know the Terminal examples in about the unit check for types of angles difference between terminal and co Goals: Co terminal reference to the circle and how comprehension and their terminal angles, and differentiate G-1.8 Rotation unit circle and terminal and co concerning measure of between degrees, minutes, and Unit Circle terminal/co terminal angles positive and rotation. seconds. CLEs Standard- terminal change directions. negative angle (Positive and N-3E, G-1A, Position illustrations direction as well Negative M-1B. Quadrennial Short class lecture as angle rotation/Terminal Radians Software with measurement in and Co terminal) Reference- presentation of corresponding degrees, minutes, Understand the Angles how angle worksheet and seconds relationship Degrees direction change examples for between Minutes fro m positive to guided practice deg/min/seconds Seconds negative 3rd quarter 2 After comp leting this unit the MA-1, MA-2, Functions Scientific Short lecture Paper and pencil weeks student will be able to understand MA-5. 1.10 Acute Angles Calculators test to Apply concepts and use the concepts of Trigonometric- Hand out demonstrate concerning the trigonometric rat ios to find the Goals: ratios Detailed Lesson worksheets for mastery of functions of values of the six t rigonometric G-3.4, G-2.3, Degrees Plan guided practice trigonometric acute and general functions for angles that measure G-2.7. Radians functions angles (Trig 30, 45, and 60 degrees. Reference- Work sheets Examine a CAD concerning ratios for 30, 45, CLEs Triangles drawing that common angles and 60 degree N-1B, N-3D, Sine CAD d rawings provide examples angles) G-1A, G-4B, Cosine of trigonometric Provide a CAD M-1B, M-2D Tangent ratios being used drawing that has Cosecant to find unknown unknown line Secant measurements lengths to be Cotangent found using Assign math trigonometric problems to check ratios for understanding II Right triangles, General triangles, Transversals, and Area of Triangles Core Concepts: Students will investigate: Right triangles using the functions sine, cosine, tangent, secant, cosecant, cotangent, and Pythagorean's theorem; The Law of Sines and Cosines to solve acute or obtuse triangles; general triangles SSS, SAS, ASA, AAS, and SSA; Problems of angle measure in reference to para llel lines cut by a transversal; and use appropriate formulas to calculate the area of a triangle. Comp. # 1 4th quarter 2 After comp leting this unit the MA-1, MA-2, Ratio Pencil The class will A test will be weeks student will be able to make a MA- 4, MA-5 Proportions Paper analyze several given to check for Be able to solve distinction between the Hypotenuse different triangles student's right triangles trigonometric rat ios of sine, cosine, Goals: Right triangle Scientific ranging fro m 30 understanding of using the secant, cosecant, tangent and G-1.6, G-1.8, Sine Calculator to 90 degrees and how to solve right functions of sine, cotangent and know the proper G-1.10, Cosine fill in a table of all triangles by hand cosine, tangent, application of each one and apply G-3. 4. G-4.1 Tangent Blank table o r ratios of sides. and by using the secant, cosecant, Pythagorean's theorem to any right Secant Spreadsheet The class will trigonometric and cotangent in triangle to find unknown sides and CLEs Cosecant then use a functions on a addition to using angles. N-1B, N-3D, Cotangent CAD d rawings of scientific scientific Pythagorean's N-3E, A-1B, Pythagorean's non-right calculator to find calculator. theorem A-1C, G-1A, theorem triangles trigonometric Students will also G-4B, and M- ratios of all be given a 2D. angles. The class blueprint with will discover that unknown the functions on measurements to the calculator are find and calculate only ratios of the and will solve sides of a triangle. several different The class will measurement then do problems exercises using using Pyth. Theor. CAD d rawings of non-right triangles Comp. # 2 4th quarter 2 Be able to construct any acute or MA-1, MA-2, Proportions Pencil The student's will A test will be weeks obtuse angle and solve for unknown MA- 4 Direct Paper solve several given to check for Be able to sides or angles with existing given Indirect triangles using the student's man ipulate informat ion using the Law of Sines Goals: Law of Sines Scientific law of Sines and understanding of formulas such as and the Law of cosines. G-1.6, G-1.8, Law of Cosines Calculator Cosines. how to solve non- the Law of Sines G-1.10, Altitude traditionaland Cosines to G-3. 4. G-4.1 Acute CAD d rawings of The student's will triangles by using solve any Obtuse non-right then develop a the law of Sines triangle whether CLEs triangles real-life scenario and cosines by right, acute, or N-1B, N-3D, using the law of hand and students obtuse in N-3E, A-1B, Poster board Sines and cosines will also be given addition to using A-1C, G-1A, to solve for a blueprint with Pythagorean's G-4B unknowns in their unknown theorem example . measurements to find and calculate Presentation of and will solve their examp le several different measurement exercises using CAD d rawings of non-right triangles Comp. # 3 4th quarter 2 After comp leting this unit the MA 1, MA 2, Congruent Co mpass Short in class The students will weeks student will be able to solve for the MA 5 Right triangle lecture with be given a CAD Solving general unknown parts of a triangle by Correspondences Protractor illustrations drawing that SSS triangles SSS, using the known parts of that same Goals: drawn on the requires a ASA SAS, ASA, triangle using the SSS, SAS, ASA, G- 1.10, 2.3, SSA Scientific - board working AAS, and SSA and AAS postulates of congruence. 3.4, 4.1, 4.6. SAS Calculator knowledge of the The students will also learn that Postulates In class math SSS, SAS, ASA, and problems special relat ionships exist between CLEs Planes Illustrations on problems with and AAS of angle pairs of angles formed when N-1B, N-3D, Lines Worksheets worksheet postulates and the measure in parallel lines are cut by a G-1A, G-4A, Parallel lines illustrations theory of reference to transversal. These concepts will be G-4B, M -2B, Converses Architect ruler transversals to parallel lines illustrated, proven, and drawn on M-2D Transversal The students will complete. cut by a Acute one or mo re CAD drawings. Co mmon- work ind ividually Obtuse transversal Alternate interior Triangles and in pairs on The students will Alternate exterior CAD d rawing that be given a written Complementary Paper/Pencil illustrate the use test to check for Supplementary CAD d rawings of these principal mastery of all Corresponding of analytical concepts geometry reviewed in this lesson plan 4th quarter 3 After comp leting this unit the MA 1, MA 2, Area Scientific - Lecture entailing all Paper and Pencil weeks student will be able to calculate the MA 4. Equilateral Calculator knowledge needed Test to illustrate Be able to area of a triangle by using the Reference- to master competency in comprehension of identify and use formulas K=1/2 bh and herons Goals: triangle Poster Examp le finding the area triangular area & the appropriate formula of K= √s(s-a)(s-b)(s-c) G- 1.8, 1.10, Semi perimeter of a possible Choose a private of several formulas for were s is equal to ½ perimeter of G-2.1, 2.3, G- Heron (Hero) business venture business venture to different triangle calculating the the triangle. 3.4, 3.8, G-4.6. Formula calculating lot calculate all figures. areas of size associated costs triangles. CLEs which will include The students will (Heron's N-1B, N-3D, Flash cards of a purchasing a be asked to draw Formula) G-1B, G-4A, business scenario triangular lot. The an aerial view of G-4B, G-2D, surface area of the their business on lot will have to be D-1C. Spread sheets for CAD and include covered with such cost justification material as marble, all the sod, or tile. measurements to their drawing& Unit Title : (Current Knowledge) Module # III Graphing trigono metric functions, calculating volu mes in English and Metric units, understanding vectors, and studying the mechanics of gears and pulleys. Core Concepts: Student will be ab le to: Recognize trigonometric functions and graph them on a graphing calculator; Calculate volumes in English and Metric units ; understand the principals of vectors ; and calculate the various arrangements and uses of gears and pulleys. Comp. # 1 5th quarter 2 After comp leting this unit the MA 1, MA 2, Radius Graphing- Lecture Written test weeks student will be able to recognize MA 4 Degrees calculator illustrating the demonstrating To interpret trigonometric function, their basic Radians differing competency in graphs of position represented by Cartesian Goal: Trig-functions Geo meter's- trigonometric recognizing the trigonometric coordinates and graph the function G 1.10, 3.4, Scale sketchpad function. different functions on a graphing calculator. 3.6 Arcs trigonometric Equivalencies Pencil and Paper Graph some trig- functions CLEs N-1B, Proportional functions on Solve vectors and how they relate N-3D, N-3E, Central-angles Graph paper graph paper Written test to to gears and pulleys Alg-2B, Alg- Period ic prove that each 3A, G-2A- G- Symmetric Handouts with Use graphing student can 4B Vectors graphic examp les calculator to make successfully Vector quantity graphs of graph a Terminal point different trig- trigonometric Directed line functions function on a segment graphing Initial point calculator and Magnitude once given a Co mponents Math worksheet graph of a problems function the student will have to write the proper corresponding trigonometric function Comp. # 2 5th quarter 2 After comp leting this unit the MA 1, MA 2, Vo lu me Many various Review volu me Students will be weeks student will be able to observe 3-D MA 5 English system size and shaped formulas for given a written To observe objects and complex containers to Metric system containers to various geometric test over volume different shaped calculate their volu mes in English G 1.10, 2.3, Area represent various shapes and sized and a container 3-D object and and Metric units 3.4, 3.6 Circu mference volumes will be given to calculate their Length The students will each onevolumes in CLEs Width Several do some paper measure and English and N-1B, N-3B, Height measuring and pencil calculate the Metric units G-1B, G-4B Depth devices problems volume G-3C, M -2C, Special Pris ms M-2D Polygon List of formu las The students will Base be asked to Lateral faces Worksheets with measure Cylinder various volume containers they Cone problems to solve brought in and Sphere calculate the Scientific volume for each calculator one using different Have students measuring devices bring an odd shaped container fro m ho me Comp. # 3 After comp leting this unit the MA-1, MA-2, Vector quantity Chapter handout Short video Written test to 5th quarter 2 student will understand vectors and MA-4 Directed line- that explains showing the prove successful To understand weeks their co mponents and be able solve segment vector operations, motion of vectors comprehension of vectors and their problems that entail the use of Goals: Initial point vectors in the fro m Math vector concepts components and vectors. G-1.7, 1.10, Terminal point rectangular Advantage use vectors to 2.1, 2.3, 3.5, Geo metric vector coordinate software The students will solve problems 4.6 Magnitude system, and the present a real life Norm properties of Lecture application of CLEs Zero Vector vectors explaining chapter using a vector N-1B, 3D, 3E, Equivalent – handouts and with ropes, G-2A, G- 4B, vector Math Advantage lesson plan pulleys, and M-2B Resultant Software weights and then Velocity vector Gu ided practice prove their Bearing Scientific g raphic of solving findings Co mponent- calculators problems. mathematically vector Real examp les ill. Projections Tension and compression 5th quarter 3 After comp leting this unit the MA-1, MA-2, Torque Bock & Tackle The students will The students will weeks student will be able to understand MA-4, MA-5 Pulleys be given a ratio print their set of To study the the phenomenon of mechanics Gears Ropes such as a (4:11 CAD d rawn gears phenomenon of involving gears and pulleys Goals: Block rear end to an and transform mechanics G-1.4, 1.8, 1- Force Co ma long automobile) and their two involving gears 10, G-2.3, 3.4, Mass be asked to design dimensional and pulleys 4.1, 4.6, Velocity List of a set of gears drawing into Gravitational- Definitions and fro m this rat io three dimensional CLEs force Formulas and then make a figures to N-1B, 3D, 3E, Freebody- drawing of their demonstrate their G-1A, 1.B, diagram Working drawing design on CAD drawing, of the 4.A, 4B, M- Tension of bevel gears with associated gears, to be of the 1B, 2D. Co mpression mathematic correct scale and Acceleration Illustrations of computations on workab le. Pitch diameter CAMS and shafts drawing Pitch circle The students will Addendum Displacement The students will print their three Base diagrams with design a pulley dimensional Root typical curves system with CA D pulley system, Radial software and print add ropes and Dedendum Disk CAM their drawings on weights to each Involute profile a 3-D printer pulley, place Throat diameter constructions scales on every Face radius rope going Bevel gear CAD software through every Central distance pulley, then Spur gear CAM gear check to see if Worm gear their measured Gear ratio CAM shaft weights match their calcu lated 3-D printer weights. If they do not the students will identify errors and make corrections IV Electrical theory, ergonomic design, load bearing capacity, and characteristics of the geometric circle Core Concepts: The Student will be able to Calculate volts, amps, watts, and ohms, create ergonomic designs such as cabinets and stairways, calculate load bearing capacity of beams and support systems, and understand the characteristics of a geometric circle. Comp. # 1 6th quarter 2 After comp leting this unit the MA 1, MA 5 Vo lts Calculator Introduce the Written test weeks student will have a general Oh ms lesson by containing (Electrical understanding of where electrical Goals: Current Worksheets explaining how problems similar Theory)– to energy originates and how such G-1.10, 2.3, Resistance energy changes to the ones calculate volts, energy changes forms. The student 2.7, 3.4, 3.8 Watts Board examp les form fro m worked in class amps, watts, and will be able to recognize electrical Gauge of wire mineral (stored) ohms as direct symbols on a blueprint, calculate CLEs Vo ltage drop Wire gauge chart energy, through a Students will be and indirect total voltage, current, ohms, and N-1A, 1C, 3D, Schemat ics process of asked to draw a proportional watts using an ohm's power wheel, 3E, M -2D, D- Blueprints Electrical CA D transformations detailed electrical units review color codes, draw electrical 1C Kilowatts drawings and until it becomes diagram in CAD symbols on a CAD drawing, Oh m's Law blueprints electrical energy. and calculate the calculate available current vs. Conductance size of their entry maximu m rating of current breaker Outlets Class lecture cable, breaker source, compare total amperage Fixtures explaining Oh m's box, and estimate used by devices, appliances, and air Switches law and how to do their monthly bill conditioning units to total available electrical in kilowatts amperage of breaker bo x, use calculations informat ion of calcu lations to determine what size of entry cable Work through to use, and estimate a dwelling's some drawing that monthly utility bill by kilowatt have numbers usage. assigned to electrical voltages, current, and resistance and calculate unknowns 2 6th quarter 2 After comp leting this unit the MA1, MA 2 Tread International Instructor will do a Students will take weeks student will be able to Create a set Riser Residential Stair demonstration of a a paper and Create of stairs so the rise and run will Goals: Step Codes wall structure and pencil test go from 1s t floor to ergonomic meet the International Residential G-1.2, 1.4, Headroom designed fro m basement. designs Code (IRS) to acco mmodate a 1.7, 1.10, 2.4, Layout Auto CAD 2009 informat ion involving given set of conditions such as a 2.7, 3.2, 4.5, Handrail Student will consult taught in the stairways and basement floor to 1st level floor. 4.7 Studs Architectural the (IRS) to lesson. cabinets The student will also be able to Elevation Draft ing and consider and design an ergonomically accessible CLEs Ergonomics Design Text calculate all Students will and/or usable set of cabinets for a N-1A, 3-D, A - Hu man motion acceptable rise draw a specified person's specific stature with an 1C, G-4A, 4B, Rise heights and tread set of steps on ergonomic design within a feasible M-2D Run lengths. A CAD accord ing comparison will be work triangle. Slope to (IRS) Codes. made to make y-intercept students aware of y = mx + b rise, run, slope and Students will y-intercept design and draw a cabinet according Students will to specificat ions. establish a median height for a family and design a cabinet layout to accommodate their physical attributes. Comp. # 3 6th quarter 2 After comp leting this unit the MA-1, MA-2 KIPS- 1000s of Text on The students will An assessment weeks student will be able to calculate lbs Architecture decide the most will be given that economical way to To calculate sizes of I beams, grades and spans Goals: Live loads residential build a basement by requires the load bearing to determine load capability. G-1.7, 1.8, Dead loads drawing and student to comparing alternate 1.10, 2.7, 3.4, Span design compare values capacity of 4.6 Joist configurations and of different calculating various beams and Beams arrangements of configurations of support CLEs N-1B, I Beams load bearing load bearing systems N-3D, 3E, G- Wide flange materials. materials on a 4A, 4B, M -2D paper and pencil test 6th quarter 3 After comp leting this unit the MA-1, MA-2, Circu mference Co mpass The students will The students will weeks student will be able to calculate the MA-5 Pi be asked to draw be given a written To study the circu mference of a circle by using Radius Protractor several circles test to show characteristics of the radius and pi, calculate the Goals: Diameter with a co mpass competency in geometric circles diameter of a circle using G-1.6, 1.8, Chord Geo metry and measure the how to calculate such as the circu mference and pi, calculate the 1.10, 2.3, 3.5, Segment worksheets diameter and circle centra, radius, area of a circle using πr², and be 4.1, Arc demonstrating circu mference of measurements diameter, able to identify the difference Tangent circles the circles and fill and will be asked circu mference, between a sector, segment, or arc. CLEs Segment out a table with to draw several sectors, N-1B, 3D, 3E, Centra Scientific these sized circles in a segments, arcs, G-1B, 4B, M- calculator measurements. practical drawing Tangents, 2D, They will then application chords, and find a co mmon according to secants ratio between the specified two known as pi. instructions The students will then be given several examples in industry of circle measurements that are required to complete a jobPost Knowledge) Higher education/career prep project Core Concept: To unite in a pro ject with at least one other program to utilize mathematical concepts learned in prev ious mathemat ics curricu lu m to provide evidential proof of mastery. To conduct a 4th Semester After comp leting this unit the MA 1, MA 2, determine, All material and Project jointly Assessment will project designed student will be able to unite with MA 3, MA 4, compare agree, resources agreed upon by be designed and and prepared by fellow students to complete a real MA 5. support, prove, available fro m trade specific designated at the a joint effort world situational workplace G 1.1, 1.2, 1.4, influence, the Cass Career instructor, CCC beginning of each between Program endeavor or task. 1.8, 1.10, 2.1, estimate, choose Center administration, project. Instructor and 2.2, 2.3, 2.7, decide justify, and core resource Math instructor 3.1, 3.2, 3.3, appraise, teachers. to demonstrate 3.5, 3.6, 3.7, interpret, build mastery of 3.8, 4.1, 4.4, disprove, test, previously 4.5, 4.6, 4.7. compile, invent, learned CLEs N-1B, solve, perceive, competencies N-1C, N-3D, influence, plan, and to N-3E, G-1A, conclude, demonstrate G-1B, G-2A, defend, evaluate, mastery of G- 4B, M- 2C, predict, measure, applicable M- 2D, rate, design, Concepts of select priorit ize mathematics. explain, criteria, assess value deduct. construct, and theorize. C&I-PacingGuide-Unit-05/08 (Content within Pacing Guide Produced by: David W. Hall
01951747 of Algorithms This text teaches the techniques needed to analyze algorithms. Organized by analysis techniques, The Analysis of Algorithms includes a systematic and largely self-contained treatment of the mathematics needed for elementary and intermediate analyses, as well as brief guides to the sources for more advanced techniques. Each technique is illustrated by being applied to the analysis of a realistic algorith. The authors provide explicit guidance on the use of various methods-for example, the discussion of mathematical induction emphasizes the process of finding the induction hypothesis, and the chapter on formulas for simplifying summations includes a section on deciding which formulas to apply. Many of the exercises give the student an opportunity to apply the techniques in developing original algorithm analyses
Linear Algebra with Applications, Sixth Edition is designed for the introductory course in linear algebra typically offered at the sophomore level. ...Show synopsisLinear Algebra with Applications, Sixth Edition is designed for the introductory course in linear algebra typically offered at the sophomore level. The new Sixth Edition is reorganized and arranged into three important parts. Part 1 introduces the basics, presenting the systems of linear equations, vectors in Rn, matrices, linear transformations, and determinants. Part 2 builds on this material to discuss general vector spaces, such as spaces of matrices and functions. Part 3 completes the course with many of the important ideas and methods in Numerical Linear Algebra, such as ill-conditioning, pivoting, and the LU decomposition. New applications include the role of linear algebra in the operation of the search engine Google and the global structure of the worldwide air transportation network have been added as a means of presenting real-world scenarios of the many functions of linear algebra in modern technology. Clear, Concise, Comprehensive - Linear Algebra with Applications, Sixth Edition continues to educate and enlighten students, providing a broad exposure to the many facets of the field49679544 BRAND NEW. PLASTIC WRAPPED. We are a tested and...New. 14496795Reviews of Linear Algebra with Applications I read the 4th edition except the starred (optional) sections. I am an economist and found little difficulty in reading this book. However, Chapter 7 is more difficult than the rest of the book, and I did not entirely understand the last example of Section 7.4. The book contains errors, but
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Book summary Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level. [via]
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Linear Algebra with Applications (8th Edition) This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra. Lay-flat type
Download Description/Abstract Dynamic geometry software promises direct manipulation of geometrical objects and relations. This paper reports aspects of a research study deigned to examine the impact of using such software on student conceptions. Analysis of the data from the study indicates that, while the use of dynamic geometry software can assist students in making progress towards more mathematical explanation (and thereby provide a foundation on which to build further notions of deductive reasoning in mathematics), the 'dynamic' nature of the software influences the form of explanation, especially in the early stages. Item Type: Book Section Additional Information: The pagination of this author's proof copy is exactly as it appears in the published version.
... read more Our Editors also recommend: The Algebraic Structure of Group Rings by Donald S. Passman "Highly recommended" (Bulletin of the London Mathematical Society) and "encyclopedic and lucid" (Bulletin of the American Mathematical Society), this book offers a comprehensive, self-contained treatment of group rings. 1985Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problems. Abstract Lie Algebras by David J Winter Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided. A Course in Algebraic Number Theory by Robert B. Ash Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition. A Course in Linear Algebra by David B. Damiano, John B. Little Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter features multiple examples, proofs, and exercises. Includes solutions to selected problems. 1988 edition. Greek Mathematical Thought and the Origin of Algebra by Jacob Klein Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography. An Introduction to Algebraic Structures by Joseph Landin This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969Product Description: gebras, group-graded rings, and the Galois theory of noncommutative rings. Suitable for advanced undergraduates and graduate students of mathematics, the text examines crossed products and group-graded rings, delta methods and semiprime rings, the symmetric ring of quotients, and prime ideals, both in terms of finite and Noetherian cases. Additional topics include group actions and fixed rings, group actions and Galois theory, Grothendieck groups and induced modules, and zero divisors and idempotents
theor... read more Customers who bought this book also bought: Our Editors also recommend: General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures. The Laplace Transform by David V. Widder This volume focuses on the Laplace and Stieltjes transforms, offering a highly theoretical treatment. Topics include fundamental formulas, the moment problem, monotonic functions, and Tauberian theorems. 1941 edition. Complex Analysis with Applications by Richard A. Silverman The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index. Undergraduate Topology by Robert H. Kasriel This introductory treatment is essentially self-contained and features explanations and proofs that relate to every practical aspect of point set topology. Hundreds of exercises appear throughout the text. 1971 edition. Point Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition. Introduction to Topology: Third Edition by Bert Mendelson Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition. Product Description: theorems and counter examples, provides a valuable reference. From explorations of topological space, convergence, and separation axioms, the text proceeds to considerations of sup and weak topologies, products and quotients, compactness and compactification, and complete semimetric space. The concluding chapters explore metrization, topological groups, and function spaces. Each subject area is supplemented with examples, problems, and exercises that progress to increasingly rigorous levels. All examples and problems are classified as essential, optional, and advanced. Reprint of the Ginn and Company, Waltham, Massachusetts, 1970
Alg linear appsDocument Transcript PrefaceHere are my online notes for my Algebra course that I teach here at Lamar University, although Ihave to admit that it's been years since I last taught this course. At this point in my career Imostly teach Calculus and Differential Equations.Despite the fact that these are my "class notes", they should be accessible to anyone wanting tolearn Algebra or needing a refresher for algebra. I've tried to make the notes as self contained aspossible and do not reference any book. However, they do assume that you've had someexposure to the basics of algebra at some point prior to this. While there is some review ofexponents, factoring and graphing it is assumed that not a lot of review will be needed to remindyou how these topics work.Here are a couple of warnings to my students who may be here to get a copy of what happened ona day that you missed.1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learnalgebra I have included some material that I do not usually have time to cover in classand because this changes from semester to semester it is not noted here. You will need tofind one of your fellow class mates to see if there is something in these notes that wasn'tcovered in class.2. Because I want these notes to provide some more examples for you to read through, Idon't always work the same problems in class as those given in the notes. Likewise, evenif I do work some of the problems in here I may work fewer problems in class than arepresented here.3. Sometimes questions in class will lead down paths that are not covered here. I try toanticipate as many of the questions as possible in writing these up, but the reality is that Ican't anticipate all the questions. Sometimes a very good question gets asked in classthat leads to insights that I've not included here. You should always talk to someone whowas in class on the day you missed and compare these notes to their notes and see whatthe differences are.4. This is somewhat related to the previous three items, but is important enough to merit itsown item. THESE NOTES ARE NOT A SUBSTITUTE FOR ATTENDING CLASS!!Using these notes as a substitute for class is liable to get you in trouble. As already notednot everything in these notes is covered in class and often material or insights not in thesenotes is covered in class. Application of Linear EquationsWe now need to discuss the section that most students hate. We need to talk about applications tolinear equations. Or, put in other words, we will now start looking at story problems or wordproblems. Throughout history students have hated these. It is my belief however that the mainreason for this is that students really don't know how to work them. Once you understand how towork them, you'll probably find that they aren't as bad as they may seem on occasion. So, we'llstart this section off with a process for working applications.Process for Working Story/Word Problems1. READ THE PROBLEM.2. READ THE PROBLEM AGAIN. Okay, this may be a little bit of overkill here.However, the point of these first two steps is that you must read the problem. This step isthe MOST important step, but it is also the step that most people don't do properly.You need to read the problem very carefully and as many times as it takes. You are onlydone with this step when you have completely understood what the problem is asking youto do. This includes identifying all the given information and identifying what you beingasked to find.Again, it can't be stressed enough that you've got to carefully read the problem.Sometimes a single word can completely change how the problem is worked. If you justskim the problem you may well miss that very important word.3. Represent one of the unknown quantities with a variable and try to relate all the otherunknown quantities (if there are any of course) to this variable.4. If applicable, sketch a figure illustrating the situation. This may seem like a silly step,but it can be incredibly helpful with the next step on occasion.5. Form an equation that will relate known quantities to the unknown quantities. To do thismake use of known formulas and often the figure sketched in the previous step can beused to determine the equation.6. Solve the equation formed in the previous step and write down the answer to all thequestions. It is important to answer all the questions that you were asked. Often you willbe asked for several quantities in the answer and the equation will only give one of them.7. Check your answer. Do this by plugging into the equation, but also use intuition to makesure that the answer makes sense. Mistakes can often be identified by acknowledgingthat the answer just doesn't make sense.Let's start things off with a couple of fairly basic examples to illustrate the process. Note as wellthat at this point it is assumed that you are capable of solving fairly simple linear equations and sonot a lot of detail will be given for the actual solution stage. The point of this section is more onthe set up of the equation than the solving of the equation. Example 1 In a certain Algebra class there is a total of 350 possible points. These points comefrom 5 homework sets that are worth 10 points each and 3 hour exams that are worth 100 pointseach. A student has received homework scores of 4, 8, 7, 7, and 9 and the first two exam scoresare 78 and 83. Assuming that grades are assigned according to the standard scale and there are noweights assigned to any of the grades is it possible for the student to receive an A in the class andif so what is the minimum score on the third exam that will give an A? What about a B?SolutionOkay, let's start off by defining p to be the minimum required score on the third exam.Now, let's recall how grades are set. Since there are no weights or anything on the grades, thegrade will be set by first computing the following percentage.actual pointsgrade percentagetotal possible points=Since we are using the standard scale if the grade percentage is 0.9 or higher the student will getan A. Likewise if the grade percentage is between 0.8 and 0.9 the student will get a B.We know that the total possible points is 350 and the student has a total points (including the thirdexam) of,4 8 7 7 9 78 83 196p p+ + + + + + + = +The smallest possible percentage for an A is 0.9 and so if p is the minimum required score on thethird exam for an A we will have the following equation.1960.9350p+=This is a linear equation that we will need to solve for p.( )196 0.9 350 315 315 196 119p p+ = = Þ = - =So, the minimum required score on the third exam is 119. This is a problem since the exam isworth only 100 points. In other words, the student will not be getting an A in the Algebra class.Now let's check if the student will get a B. In this case the minimum percentage is 0.8. So, tofind the minimum required score on the third exam for a B we will need to solve,1960.8350p+=Solving this for p gives,( )196 0.8 350 280 280 196 84p p+ = = Þ = - =So, it is possible for the student to get a B in the class. All that the student will need to do is getat least an 84 on the third exam. Example 2 We want to build a set of shelves. The width of the set of shelves needs to be 4times the height of the set of selves and the set of shelves must have three shelves in it. If thereare 72 feet of wood to use to build the set of shelves what should the dimensions of the set ofshelves be?SolutionWe will first define x to be the height of the set of shelves. This means that 4x is width of the setof shelves. In this case we definitely need to sketch a figure so we can correctly set up theequation. Here it is,Now we know that there are 72 feet of wood to be used and we will assume that all of it will beused. So, we can set up the following word equation.length of length of72vertical pieces horizontal piecesæ ö æ ö+ =ç ÷ ç ÷è ø è øIt is often a good idea to first put the equation in words before actually writing down the equationas we did here. At this point, we can see from the figure there are two vertical pieces; each onehas a length of x. Also, there are 4 horizontal pieces, each with a length of 4x. So, the equation isthen,( ) ( )4 4 2 7216 2 7218 724x xx xxx+ =+ ===So, it looks like the height of the set of shelves should be 4 feet. Note however that we haven'tactually answered the question however. The problem asked us to find the dimensions. Thismeans that we also need the width of the set of shelves. The width is 4(4)=16 feet. So thedimensions will need to be 4x16 feet.Pricing ProblemsThe next couple of problems deal with some basic principles of pricing.Example 3 A calculator has been marked up 15% and is being sold for $78.50. How much didthe store pay the manufacturer of the calculator?SolutionFirst, let's define p to be the cost that the store paid for the calculator. The stores markup on thecalculator is 15%. This means that 0.15p has been added on to the original price (p) to get theamount the calculator is being sold for. In other words, we have the following equation0.15 78.50p p+ = that we need to solve for p. Doing this gives,78.501.15 78.50 68.260871.15p p= Þ = =The store paid $68.26 for the calculator. Note that since we are dealing with money we roundedthe answer down to two decimal places.Example 4 A shirt is on sale for $15.00 and has been marked down 35%. How much was theshirt being sold for before the sale?SolutionThis problem is pretty much the opposite of the previous example. Let's start with defining p tobe the price of the shirt before the sale. It has been marked down by 35%. This means that 0.35phas been subtracted off from the original price. Therefore, the equation (and solution) is,0.35 15.000.65 15.0015.0023.07690.65p ppp- === =So, with rounding it looks like the shirt was originally sold for $23.08.Distance/Rate ProblemsThese are some of the standard problems that most people think about when they think aboutAlgebra word problems. The standard formula that we will be using here isDistance Rate Time= ´All of the problems that we'll be doing in this set of examples will use this to one degree oranother and often more than once as we will see.Example 5 Two cars are 500 miles apart and moving directly towards each other. One car ismoving at a speed of 100 mph and the other is moving at 70 mph. Assuming that the cars startmoving at the same time how long does it take for the two cars to meet?SolutionLet's let t represent the amount of time that the cars are traveling before they meet. Now, weneed to sketch a figure for this one. This figure will help us to write down the equation that we'llneed to solve.From this figure we can see that the Distance Car A travels plus the Distance Car B travels mustequal the total distance separating the two cars, 500 miles. Here is the word equation for this problem in two separate forms.Distance Distance500of Car A of Car BRate of Time of Rate of Time of500Car A Car A Car B Car B used the standard formula here twice, once for each car. We know that the distance a cartravels is the rate of the car times the time traveled by the car. In this case we know that Car Atravels at 100 mph for t hours and that Car B travels at 70 mph for t hours as well. Plugging theseinto the word equation and solving gives us,100 70 500170 5005002.941176 hrs170t ttt+ === =So, they will travel for approximately 2.94 hours before meeting.Example 6 Repeat the previous example except this time assume that the faster car will start 1hour after slower car starts.SolutionFor this problem we are going to need to be careful with the time traveled by each car. Let's let tbe the amount of time that the slower travel car travels. Now, since the faster car starts out 1 hourafter the slower car it will only travel for 1t - hours.Now, since we are repeating the problem from above the figure and word equation will remainidentical and so we won't bother repeating them here. The only difference is what we substitutefor the time traveled for the faster car. Instead of t as we used in the previous example we willuse 1t - since it travels for one hour less that the slower car.Here is the equation and solution for this example.( )100 1 70 500100 100 70 500170 6006003.529412 hrs170t tt ttt- + =- + === =In this case the slower car will travel for 3.53 hours before meeting while the faster car will travelfor 2.53 hrs (1 hour less than the faster car…). Example 7 Two boats start out 100 miles apart and start moving to the right at the same time.The boat on the left is moving at twice the speed as the boat on the right. Five hours after startingthe boat on the left catches up with the boat on the right. How fast was each boat moving?SolutionLet's start off by letting r be the speed of the boat on the right (the slower boat). This means thatthe boat to the left (the faster boat) is moving at a speed of 2r. Here is the figure for this situation.From the figure it looks like we've got the following word equation.Distance Distance100of Boat B of Boat Aæ ö æ ö+ =ç ÷ ç ÷è ø è øUpon plugging in the standard formula for the distance gives,Rate of Time of Rate of Time of100Boat B Boat B Boat A Boat Aæ öæ ö æ öæ ö+ =ç ÷ç ÷ ç ÷ç ÷è øè ø è øè øFor this problem we know that the time each is 5 hours and we know that the rate of Boat A is 2rand the rate of Boat B is r. Plugging these into the work equation and solving gives,( )( ) ( )( )100 5 2 5100 5 10100 520r rr rrr+ =+ ===So, the slower boat is moving at 20 mph and the faster boat is moving at 40 mpg (twice as fast).Work/Rate ProblemsThese problems are actually variants of the Distance/Rate problems that we just got doneworking. The standard equation that will be needed for these problems is,Portion of job Work Time Spentdone in given time Rate Workingæ ö æ ö æ ö= ´ç ÷ ç ÷ ç ÷è ø è ø è øAs you can see this formula is very similar to the formula we used above. Example 8 An office has two envelope stuffing machines. Machine A can stuff a batch ofenvelopes in 5 hours, while Machine B can stuff a batch of envelopes in 3 hours. How longwould it take the two machines working together to stuff a batch of envelopes?SolutionLet t be the time that it takes both machines, working together, to stuff a batch of envelopes. Theword equation for this problem is,Portion of job Portion of job1 Jobdone by Machine A done by Machine BWork Rate Time Spent Work Rate Time Spent1of Machine A Working of Machine B know that the time spent working is t however we don't know the work rate of each machine.To get these we'll need to use the initial information given about how long it takes each machineto do the job individually. We can use the following equation to get these rates.Work Time Spent1 JobRate Workingæ ö æ ö= ´ç ÷ ç ÷è ø è øLet's start with Machine A.( ) ( )11 Job Work Rate of A 5 Work Rate of A5= ´ Þ =Now, Machine B.( ) ( )11 Job Work Rate of B 3 Work Rate of B3= ´ Þ =Plugging these quantities into the main equation above gives the following equation that we needto solve.1 11 Multiplying both sides by 155 33 5 158 15151.875 hours8t tt ttt+ =+ === =So, it looks like it will take the two machines, working together, 1.875 hours to stuff a batch ofenvelopes.Example 9 Mary can clean an office complex in 5 hours. Working together John and Mary canclean the office complex in 3.5 hours. How long would it take John to clean the office complexby himself?SolutionLet t be the amount of time it would take John to clean the office complex by himself. The basicword equation for this problem is, Portion of job Portion of job1 Jobdone by Mary done by JohnWork Rate Time Spent Work Rate Time Spent1of Mary Working of JohnThis time we know that the time spent working together is 3.5 hours. We now need to find thework rates for each person. We'll start with Mary.( ) ( )11 Job Work Rate of Mary 5 Work Rate of Mary5= ´ Þ =Now we'll find the work rate of John. Notice however, that since we don't know how long it willtake him to do the job by himself we aren't going to be able to get a single number for this. Thatis not a problem as we'll see in a second.( ) ( )11 Job Work Rate of John Work Rate of Johntt= ´ Þ =Notice that we've managed to get the work rate of John in terms of the time it would take him todo the job himself. This means that once we solve the equation above we'll have the answer thatwe want. So, let's plug into the work equation and solve for the time it would take John to do thejob by himself.( ) ( )( )( )1 13.5 3.5 1 Multiplying both sides by 553.5 3.5 5 517.5 1.517.511.67 hrs1.5ttt ttt t+ =+ === Þ =So, it looks like it would take John 11.67 hours to clean the complex by himself.Mixing ProblemsThis is the final type of problems that we'll be looking at in this section. We are going to belooking at mixing solutions of different percentages to get a new percentage. The solution willconsist of a secondary liquid mixed in with water. The secondary liquid can be alcohol or acidfor instance.The standard equation that we'll use here will be the following.Amount of secondary Percentage of Volume ofliquid in the water Solution Solutionæ ö æ ö æ ö= ´ç ÷ ç ÷ ç ÷è ø è ø è øNote as well that the percentage needs to be a decimal. So if we have an 80% solution we willneed to use 0.80. Example 10 How much of a 50% alcohol solution should we mix with 10 gallons of a 35%solution to get a 40% solution?SolutionOkay, let x be the amount of 50% solution that we need. This means that there will be 10x +gallons of the 40% solution once we're done mixing the two.Here is the basic work equation for this problem.( ) ( ) ( )Amount of alcohol Amount of alcohol Amount of alcoholin 50% Solution in 35% Solution in 40% SolutionVolume of Volume of Volume of0.5 0.35 0.450% Solution 35% Solution 40% Soæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è øæ ö æ ö+ =ç ÷ ç ÷è ø è ø lutionæ öç ÷è øNow, plug in the volumes and solve for x.( ) ( )0.5 0.35 10 0.4 100.5 3.5 0.4 40.1 0.50.55gallons0.1x xx xxx+ = ++ = +== =So, we need 5 gallons of the 50% solution to get a 40% solution.Example 11 We have a 40% acid solution and we want 75 liters of a 15% acid solution. Howmuch water should we put into the 40% solution to do this?SolutionLet x be the amount of water we need to add to the 40% solution. Now, we also don't how muchof the 40% solution we'll need. However, since we know the final volume (75 liters) we willknow that we will need 75 x- liters of the 40% solution.Here is the word equation for this problem.Amount of acid Amount of acid Amount of acidin the water in 40% Solution in 15% Solutionæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è øNotice that in the first term we used the "Amount of acid in the water". This might look a littleweird to you because there shouldn't be any acid in the water. However, this is exactly what wewant. The basic equation tells us to look at how much of the secondary liquid is in the water. So,this is the correct wording. When we plug in the percentages and volumes we will think of thewater as a 0% percent solution since that is in fact what it is. So, the new word equation is,( ) ( ) ( )Volume Volume of Volume of0 0.4 0.15of Water 40% Solution 15% Solutionæ ö æ ö æ ö+ =ç ÷ ç ÷ ç ÷è ø è ø è ø Do not get excited about the zero in the first term. This is okay and will not be a problem. Let'snow plug in the volumes and solve for x.( )( ) ( )( ) ( )( )0 0.4 75 0.15 7530 0.4 11.2518.75 0.418.7546.875 liters0.4x xxxx+ - =- === =So, we need to add in 46.875 liters of water to 28.125 liters of a 40% solution to get 75 liters of a15% solution.
This book connects coding theory with actual applications in consumer electronics and with other areas of mathematics. Different Aspects of Coding Theory covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science. Features: A unique combination of mathematical theory and engineering practice. Much diversity and variety among chapters, thus offering broad appeal.
Gauss-Kronrod Integration is an adaptation of Gaussian quadrature used on some graphing calculators. This Java applet outlines the mathematical computations involved and visually demonstrates the process the calculator uses to evaluate the integral. Marden's Theorem concerns the relative positions of the roots of a cubic polynomial and those of its derivative. This article gives a proof of Marden's theorem, along with dynamic geometry animations and some of the history of the result. This utility uses the free Flash player plug-in resident in most browsers to allow the user to plot a parametrically defined surface on a customized scale and dynamically rotate the three-dimensional picture. These applets provide interactive student activities to make connections between the graphical and analytical interpretation of "completing the square" and writing the equation of a parabola in general and standard form.
Questions About This Book? The Used copy of this book is not guaranteed to inclue any supplemental materials. Typically, only the book itself is included. Summary This book provides readers with a solid understanding of the definitions and principles of trigonometry and their application to problem solving. Identities are introduced early in Chapter 1. They are reviewed often and are then covered in more detail in Chapter 5. Also, exact values of the trigonometric functions are emphasized throughout the book. There are numerous calculator notes placed throughout the book.
Synopses & Reviews Publisher Comments: Since the publication of the first edition, Mathematica has matured considerably and the computing power of desktop computers has increased greatly. This enables the presentation of more complex curves and surfaces as well as the efficient computation of formerly prohibitive graphical plots. Incorporating both of these aspects, CRC Standard Curves and Surfaces with Mathematica, Second Edition is a virtual encyclopedia of curves and functions that depicts nearly all of the standard mathematical functions rendered using Mathematica. While the easy-to-use format remains unchanged from the previous edition, many chapters have been reorganized and better graphical representations of numerous curves and surfaces have been produced. An introductory chapter describes the basic properties of curves and surfaces, includes two handy tables of 2-D and 3-D curve and surface transformations, and provides a quick understanding of the basic nature of mathematical functions. To facilitate more efficient and more thorough use of the material, the whole gamut of curves and surfaces is divided into sixteen individual chapters. The accompanying CD-ROM includes Mathematica notebooks of code to construct plots of all the functions presented in the book. Expanded index for quick access to curves or surfaces of interest and to find definitions of common mathematical terms Upgraded Mathematica notebooks with more uniform formatting, more complete documentation on particular curves and surfaces, an explanation of the plotting algorithms, and more explicit designations of variable parameters to easily adjust curve or surface plots Synopsis: Synopsis: "Synopsis" by Ingram,"Synopsis" by Ingram,
The Mathematical Association of America's online Digital Classroom site offers no faint praise for this interactive set of tools, noting that "it is exciting, fast, and fully object-oriented". This is all true, and... Problems With a Point is a site developed for mathematics students and teachers in grades 6-12. The site contains practice problems on various topics that designed to help students understand mathematical concepts and... A short article designed to provide an introduction to functional equations, those in which a function is sought which is to satisfy certain relations among its values at all points. For example, we may look for... Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. Organized into the topics of sets and relations, infinity and induction, sequences of numbers,...
Basic Mathematical Skills with Geometry Basic Mathematical Skills with Geometry, 9/e, by Baratto, Bergman, and Hutchison is part of the latest offerings in the successful Hutchison Series ...Show synopsisBasic Mathematical Skills with Geometry, 9/e, by Baratto, Bergman, and Hutchison is part of the latest offerings in the successful Hutchison Series in Mathematics. The book is designed for a one-semester course in basic math and is appropriate for lecture, learning center, laboratory, and self-paced settings. The ninth edition continues the series' hallmark approach of encouraging mastery of mathematics through careful practice. The text provides detailed, straightforward explanations and accessible pedagogy to help students grow their math skills from the ground up. The authors use a three-pronged approach of communication, pattern recognition, and problem solving to present concepts understandably, stimulate critical-thinking skills, and stress reading and communication skills in order to help students become effective problem-solvers. Features such as Tips for Student Success, Check Yourself exercises, and Activities underscore this approach and the underlying philosophy of mastering math through practice. Exercise sets have been significantly expanded and are now better-organized, and applications are now more thoroughly integrated throughout the text. The text is fully-integrated with McGraw-Hill's online learning system, Connect Math Hosted by ALEKS Corp, and is available with ALEKS 360 Ships same or next business day with delivery...Acceptable. Ships same or next business day with delivery confirmation. Acceptable condition. Contains highlighting. Expedited shipping available. Description:Good. Paperback. May include moderately worn cover, writing,...Good. Paperback. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780073384443-4Fine. Paperback. Almost new condition. SKU: 9780073384443-2-0-3...Fine. Paperback. Almost new condition. SKU: 9780073384443-2
Find a Mt Vernon, NY CalculusSame goes for discrete mathematics. In mathematics we call things discrete if they involve: The set of integers, the set of whole numbers, or the set of natural numbers. Where as we tend to call something continuous if it involves the set of real numbers
Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.
Suggestions for Studying for Exam 2 The final exam will cover all of the material we covered this semester, with an emphasis on the material we've done since the last exam. A good way to study for this quiz is to try doing some of the review problems at the end of each chapter. You may use your calculator as long as it is a TI83/84 Plus or TI83/84 Plus Silver Edition, or has similar capabilities. You may not use a TI/89 on the exam. If you have a calculator other than a TI83/84 Plus or TI83/84 Plus Silver Edition, please talk with me. You may prepare a single page of notes (one side of the paper only) to bring with you to the final. Additionally, you may bring your note cards from the previous two exams. You will be tested on three main topics: Limits Calculate limits using tables, graphs, and algebra Be able to identify when and explain why a limit doesn't exist Derivatives Find the derivative of a function by using the limit definition Find the derivative of a function by using the rules for differentiating Find the derivative of an inverse function Graph the derivatives of a function given the graph of the function (and vice versa) Determine information about the graph of a function (concavity, increasing/decreasing) given information about the first and second derivatives Determine the units of and interpret first and second derivatives as velocity, acceleration, a rate of change, or the rate that a rate of change is changing. Find the line tangent to a curve at a given point Find the tangent line approximation to a function and estimate the error Functions Determine if a graph is the graph of a linear function, a polynomial function, or an exponential function Determine if a table of values gives the values of a linear function, an exponential function, or something else Having determined what kind of function the graph or table defines, find the formula for it Graph polynomials, power functions, linear functions, and exponential functions, given the formula
UNIT-II: ALGEBRA 1. Matrices: (18) Period Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). 2. Determinants: (20) Periods Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. 2. Applications of Derivatives: (10) Periods Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). 3. Integrals: (20) Periods Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, simple integrals to be evaluated. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4. Applications of the Integrals: (10) Periods Applications in finding the area under simple curves, especially lines, circles/parabolas/ ellipses (in standard form only), Area between the two above said curves (the region should be clearly identifiable). 5. Differential Equations: (10) Periods Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx + py = q where p and q are functions of x or constant + px = q, where p and q are functions of y or constant UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY 1. Vectors: (12) Periods Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors. Scalar triple product of vectors. 2. Three - dimensional Geometry: (12) Periods Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane
Mathematics Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges. Students who achieve the 28–32 level are likely able to use variables fluently so that they can solve problems with variables in the same way that they can solve the problems with numbers, and they can use variables to represent general properties. Because of the close connections between Algebra and Functions, several Standards apply to both. These Standards are marked by asterisks and listed in both categories.Match simple inequalities with their graphs on the number line (e.g., x ≥ – ) Exhibit knowledge of slope Match linear equations with their graphs in the coordinate plane* Recognize that when numerical quantities are reported in real-world contexts, the numbers are often rounded Solve real-world problems by using first-degree equations Solve first-degree inequalities when the method does not involve reversing the inequality sign Match compound inequalities with their graphs on the number line (e.g., –10.5 < x ≤ 20.3) Add, subtract, and multiply polynomials Identify solutions to simple quadratic equations Solve quadratic equations in the form (x + a)(x + b) = 0, where a and b are numbers or variables Extend a given pattern by a few terms for patterns that have a constant factor between terms
The Developmental Mathematics workbook series covers basic mathematics through early algebra. Workbooks aren't grade-specific, but rather focus on individual skills, making it an ideal curriculum for self-paced learners at any ability level. This is a self-teaching curriculum that was specifically designed for students to read, learn, and complete themselves, cultivating independent learning skills. Lessons begin with an explanation of the concept and example problems that are solved step-by-step. A number of practice problems are provided on the following "Applications" pages. 80 pages, softcover. Student workbook only; levels are not grade specific. Skills are early elementary. A diagnostic test is included Developmental Math, Level 2, Student Workbook Review 1 for Developmental Math, Level 2, Student Workbook Overall Rating: 5out of5 Date:October 25, 2007 Maria Toral This series is great for teaching children basic mathematics! Though it may appear to progress slowly, the children develop a thorough understanding of the material. May be advanced quickly for gifted students, used along with manipulatives for the average student, and a lesson can be spread over multiple days for the slower learner.
Calculus for the Utterly Confused - 2nd edition Summary: Whether you're a science major, an engineer, or a business graduate, calculus can be one of the most intimidating subjects around. Fortunately, Calculus for the Utterly Confused is your formula for success. Written by two experienced teachers who have taken the complexity out of calculus for thousands of students, this book breaks down tough concepts into easy-to-understand chunks. Calculus for the Utterly Confused shows you how to apply calculus concepts to p...show moreroblems in business, medicine, sociology, physics, and environmental science. You'll get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time! Inside, you'll learn about Calculus problems with applications to business and economics How to use spreadsheets for business analysis Growth and decay models including exponential and logarithmic models for biology
Students in need of experience constructing and interpreting statistical graphs will find this exercise useful. The lesson uses data from past presidential elections; students will construct a variety of graphs (bar... This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered...
Sign in to YouTube This is the full first lecture of a course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really ``Linear Algebraic Geometry'': so teaching the algebra without the geometry is depriving the student of the heart of the subject. The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates! Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!
General Study Strategies Studying Math is Different from Studying Other Subjects Math is learned by doing problems. Do the homework. The problems help you learn the formulas and techniques you do need to know, as well as improve your problem-solving prowess. A word of warning: Each class builds on the previous ones, all semester long. You must keep up with the instructor: attend class, read the text, and do homework every day. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep trouble. A word of encouragement: Each class builds on the previous ones, all semester long. You're always reviewing previous material as you do new material. Many of the ideas hang together. Identifying and learning the key concepts means you don't have to memorize as much. Math is a skill. To develop that skill you must practice. Do your homework in a quiet place, similar to the classroom if possible. Do not spend "hours" on one problem. If you cannot solve a problem, look for a similar problem in your notes or your text. If you still cannot solve a problem, skip it and work on other problems. Try the problem later. Many times you will come up with an idea after you have done something else for a while. If you still cannot solve the problem, get some help. Math Study Skills: Active Learning Be actively involved in your education! Here are some tips to "take charge" of learning in a math class: Take responsibility for studying, recognizing what you do and don't know, and knowing how to get your instructor to help you with what you don't know. Attend class every day and take complete notes. Instructors formulate test questions based on material and examples covered in class as well as on those in the text. Be an active participant in the classroom. Get ahead in the book; try to work some of the problems before they are covered in class. Anticipate what the Instructor's next step will be. Ask questions in class! There are usually other students wanting to know the answers to the same questions you have. Go to office hours and ask questions. The instructor will be pleased to see that you are interested and you will be actively helping yourself. Keep a glossary of math terms as they are presented in class. Math is a language; maintain a list of terms to keep you involved and learning. Show ALL work; do not skip steps, even on homework. Good study habits throughout the semester make it easier to study for tests.
igonometry: A Unit Circle Approach A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using ...Show synopsisA proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of most readers. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Chapter topics include Functions and Their Graphs; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Exponential and Logarithmic Functions; and more. For anyone interested in trigonometry.Hide synopsis. 0321716574 covers and corners may show shelf wear used...Fine. 0321716574 covers and corners may show shelf wear used books may be missing software and or codes. spirals will show more wear because of nature of book. Description:New. No dust jacket. Audience: General/trade. NOTE This is an...New. No dust jacket. Audience: General/trade. NOTE This is an annotated instructor's edition. It is the same as the student edition with the addition of exercise answers. That is the only way in which it differs. NOTE
Summary: Math 320 (spring 2011) About the second midterm Here is a list of the topics which we have covered in class since the previous midterm. You should also see also the assigned homework problems on the course web page. Linear algebra The definition of linear independence. Know the definition (see page 248). "Know the definition" means "know the definition," i.e., if you are asked for the definition, then you should be able to state it. Know how to use the definition (in combination with row reduction) to prove a given list of vectors is independent or not (as in examples 5 and 6 on pages 249250.) Linear algebra subspaces. Know the definition: in this course we have adopted theorem 1 on page 241 as the definition. Be able to prove/disprove that a given set S is a linear subspace of Rn . Be able to find a basis for the solution space of a given set of linear equations (see the algorithm and example on pages 258/259). You should also know the definition of a basis, and you should know the defi- nition of when a set of vectors spans a given subspace. The above topics are covered in the book in §§4.24.4. Differential equations first order. You should know how to solve separable equations (y = f(x)g(y), see §1.4) and linear equations (y + P(x)y = Q(x), see §1.5). None of this is new, as you have already seen this material in math 222.
Secondary Curricula Algebra II core Instruction for all students. Carnegie Learning Algebra II promotes the understanding of both linear and non-linear functional forms, as well as the relationship between text, equations, graphs and tables through the mathematical modeling of realistic situations. Our program motivates students to talk about mathematical functions, tackle real-world problems, strengthen their conceptual foundations and understand Algebra's relevance in everyday life. Please use the tabs below to learn more about the features and contents of this curricula and its various implementation options. Use the content browser on the left to view videos and image galleries of the curricula. Searching for Patterns Quadratic Functions Graphs of Polynomial Functions Polynomial Expressions and Equations Polynomial Modeling Sequences and Series Graphs of Rational Functions Rational Expressions and Equations Radical Functions Graphs of Exponential and Logarithmic Functions Exponential and Logarithmic Expressions and Equations Mathematical Modeling Graphs of Trigonometric Functions Trigonometric Expressions and Equations Interpret Data in a Normal Probability Distribution Make Inference and Justify Conclusions Make Decisions Using Complex Probability Models own their learning making notes as they learn and using their books as II content can be delivered in a blended course format, with a combination of collaborative, student-centered textbook lessons and adaptive Cognitive Tutor software lessons. Can be used as core instruction. Carnegie Learning Algebra II content can be delivered via textbooks that support a collaborative classroom. Our classroom activities address both mathematical content and process standards. Students develop skills to work cooperatively to solve problems and improve their reasoning and communication skills. Our Algebra II content is available in our Adaptive Math Software Solutions, which are packages that feature our research-based Cognitive Tutor Software product line. Available in both the Carnegie Learning Adaptive High School Solution and the Carnegie Learning Adaptive Secondary Math Solution. I think the biggest difference with this curriculum is definitely student attitude. They are so excited. I have so many more students that now say that math is their favorite subject and their favorite class, and that usually is not the case.
Computational Physics Introduction 3/30/11 Goals  Calculate solutions to physics problems  All physics problems can be formulated mathematically.  Many strategies for solving equations.  Display solutions in a way that helps us interpret the physics Division of Labor  Most of the work in solving a problem is still done in the physicist's head  Derive the equations that represent the system of interest  Understand all the approximations and limitations (conditions for validity)  Determine how to instruct the computer to solve the equations  The computer does what it is told to do.  The physicist has to interpret the computer's output  Computational solutions are theoretical predictions (based on the equations). They must eventually be compared to measurements. equations  Many types of equations: 2 x  Algebraic y  5x  2 y L L  Trigonometric, logorithmic tan 2c  tanh 2c  2y Ek 2  4 y  Differential, integral t 2   x 4   Linear, nonlinear  You may have a set of equations that must  be solved simultaneously  Matrix manipulations, linear algebra  Your equations may depend on initial conditions or boundary conditions Solving equations  Some special equations have an analytical, or "closed-form," solution, which is a certain known function or combination of functions. d2 p 2  2p  0  p(t)  Asin(t   ) dt  Most equations (or sets of equations) must be solved numerically, using a computer. The  resulting solution is approximate, and consists only of a set of numbers Visualizing results  In most cases, you will want to make a plot of the solution, in order to visualize how certain quantities depend on others.  This is something that a computer is especially good at. Strategies  Programs such as Mathematica and MATLAB can help you work with equations analytically  Symbolic manipulation  Might help you obtain analytical solution  Most physics problems (that are not highly simplified) involve equations that must be solved numerically.  Smooth funtions must be discretized  Derivatives become differences  Integrals become sums  Errors of approximation must be carefully tracked Numerical solutions  Can be done with Mathematica or MATLAB  Actual solving strategies are built in  Need to understand limitations  Can use a scientific programming language such as FORTAN or C  Many basic strategies have already been written  Use library of routines - customize to your problem  Solution must be plotted to be useful  Special graphics programs are available  Mathematica & MATLAB do this well, too
College Geometry A Problem-Solving Approach With Applications 9780131879690 ISBN: 0131879693 Edition: 2 Pub Date: 2007 Publisher: Prentice Hall Summary: For courses in Geometry or Geometry for Future Teachers. This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidea...n geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections. Musser, Gary is the author of College Geometry A Problem-Solving Approach With Applications, published 2007 under ISBN 9780131879690 and 0131879693. Five hundred ninety six College Geometry A Problem-Solving Approach With Applications textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $48.69, or buy new starting at $115
Math Course Takes 'Real Life' Approach to Algebra Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life." Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts. The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback
This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high... More > schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.< Less Students will naturally ask, "When will I use this stuff?" With some mathematical concepts, the answer will be a definite "Never!" However, it is very likely you will... More > require trigonometry in some form. You may only need some of the trigonometry topics, but applications similar to the ones contained in this book will probably be required. One of my students worked with a construction firm. He was required to determine whether or not the dump trucks would be in any danger of hitting the overhead hydro wires, preferably with an accurate solution. This book is designed to teach the skills required to be successful solving problems involving triangles. It is suitable for an independent learner, a student in a class, parent, tutor, or for a teacher.< Less Ray's Treatise on Geometry and Trigonometry. 421 pages. Begins by giving definitions for some basic geometrical terms, then begins Geometry, starting with parallel lines, then continuing with Arcs... More > and Radii, the properties of triangles, Parallelograms, measuring area, Polygons, the geometry of space, Pyramids, Prisms, etc. The book then continues on into the subject of Trigonometry, and supplies logarithmic tables. No problems are supplied for the student in this book, which instead gives all it's attention to teaching the concepts. It is suggested that the student use another book to provide problems while learning the mathematical processes from this book.< Less This book is a great way to practice concepts in beginning trigonometry. Topics such as converting degrees and radians, finding area and arc length of sectors, Pythagorean Theorem, and right... More > triangle trigonometry.< Less
Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized... more... The aim of this book is to throw light on various facets of geometry through development of four geometrical themes.The first theme is about the ellipse, the shape of the shadow cast by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola.The third theme... more... The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions,... ? and everything in between ? CliffsQuickReview Geometry can help you make sense of it all. ThisMathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch,... more...
Summary: Practical Business Math Proceduresis a comprehensive introduction to the concepts and applications of mathematics to personal and commercial business problems. The text uses basic arithmetic and problem solving techniques and illustrates their use in retailing, interest and loans, banking, payroll, taxes, investments, insurance, and a variety of other business situations. The text is well known for the motivating integration of interesting real world examples and photos from the Wall...show more Street Journal, Kiplinger's, and many other business journals.Slateris the most popular and widely used book for this course and is carefully written and developed to support students with little math experience with practice quizzes, thousands of exercises, color coded procedures and diagrams, supporting tutorial videos on DVD, and the highest standards of reliability and cleanliness. ...show less Book in almost Brand New condition528540
Algebra Glencoe Lesson BIGIDEA: NUMBERS, OPERATIONS AND EXPRESSIONS Students work with integer exponents, scientific notation, and radicals, and use variables and expressions to solve problems from purely mathematical as well as applied contexts. Algebra: BIGIDEA2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals. Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties. BigIdea: The place values to the right of the decimal point in the base-ten system names numbers less than one. EQ: ... MG 2.1* MG 2.2* Algebra and Functions ⅔** AF 2.1* prescription for determining a second number when a first number is given. BigIdea2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes. ... Supporting Idea: Algebra Supporting Idea: Geometry and Measurement Supporting Idea: Number and Operations Hear about the big ideas behind this book. Do several key activities: fractions ... that remove the abstraction from algebra and give it meaning. Topics will be from algebra 1& 2, trigonometry, & pre-calculus. Modeling With Geometry and the 8 Mathematical ... A Unifying Idea = The Equal Sign ... with their college and career goals for 5 years as part of a non-profit program she developed called, TeenSpace. The idea to ... Carol previously taught Algebra2, ... Big Brothers Big Sisters of Athens County, OUCTM, and the National Hands on Network. Scanlon, Rick (540)720-4100 Math ... Participants will consider the alternative energy as a means for exploration and the math concepts that such an idea will entail. ... Developing Big Ideas in Algebra thru ... We have examples for use in Algebra 1 & 2, geometry, and Calculus that we have copied ... ... for GOAL SETTING purposes and represent a suggestion of how long it should take students to acquire a specific content idea or ... using inspection, long division, or a computer algebra system for more complex ... · Major understandings are the big generalizations for the topic ... GLE captures the bigidea (conceptual understanding) of magnitude of numbers. CCSS is ... a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a ... -- Use appropriate representations to solve problems or to portray, clarify, or extend a mathematical idea. JASPER PRE-ALGEBRA WORKING SMART X All 3 episodes help students see the power of ... A CAPITAL IDEA ACI involves a sample within a ... It involves discover a mutual interest in finding a way to 2 sampling methods and 1 extrapolation to the carry on funding for the 9th grade school trip to But perhaps the most provocative idea is the proposal for adopting rule 137, ... NCAA football ratings determine which schools get to play for the big money in postseason bowl games. ... Progress in Commutative Algebra2 : ... ... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs to be ... How Big is 1 Million? 8A 12A 16A Expanded Notation 18A ... ALGEBRA & FUNCTIONS AF1.2...Expressions with Parenthesis ... ... How Big is 1,000? Problem Solving: Number ... take the DSAT Exam and look over the CST "Released Questions" prior to planning your lessons so that you have a good idea of the level of teaching that needs ... ALGEBRA & FUNCTIONS...CLUSTER 3 NUMBER SENSE... CLUSTER 2 NUMBER SENSE ... This session will focus on meaningful algebra activities that are concrete ... lesson, including the NJ Standards, will be discussed. See an idea today - use it in your ... This session will focus on a curriculum organized around the "big ideas" of Algebra and help your students ...
7 Further reading and sources of help Further reading The Good Study Guide, by Andrew Northedge published by The Open University, 1990, ISBN 0 7492 00448. Chapter 4 is entitled – 'Working with numbers'. Other chapters are 'Reading and note taking', 'Other ways of studying', 'What is good writing?', 'How to write essays', 'Preparing for examinations' The Sciences Good Study Guide, by Andrew Northedge, Jeff Thomas, Andrew Lane, Alice Peasgood, published by The Open University, 1997, ISBN 0 7492 341 1 3. More mathematical and science-based than The Good Study Guide. Chapter titles are: 'Getting started', 'Reading and making notes', 'Working with diagrams', 'Learning and using mathematics', 'Working with numbers and symbols', 'Different ways of studying', 'Studying with a computer', 'Observing and experimenting', 'Writing and tackling examinations', followed by 100 pages of 'Maths help' on: calculations, negative numbers, fractions, decimals, percentages, approximations and uncertainties, powers and roots, scientific notation, formulas and algebra, interpreting and drawing graphs, and perimeters, areas and volumes. Breakthrough to Mathematics, Science and Technology (K507) – only available from the Open University. Module 1, entitled 'Thinking about measurement', looks at mathematics in a variety of contexts, e.g. in the kitchen, on the road, in the factory, in the natural world. Module 4, entitled 'Exploring pattern', looks at geometrical and numerical patterns using everyday examples. The other four modules in the series have a greater emphasis on science or technology than on mathematics. Each module refers to The Sciences Good Study Guide. Teach yourself basic mathematics, by Alan Graham, Hodder and Stoughton, London, 1995, ISBN 0 340 64418 4. A book aimed at a more general (i.e. non-OU) audience is in two parts entitled 'Understanding the basics' and 'Maths in action'. Countdown to mathematics Volume 1, by Lynne Graham and David Sargent, Addison-Wesley, Slough, 1981, ISBN 0 201 13730 5. This is a useful next stage after any of the above and includes an introduction to algebra. Investigating Statistics: a beginner's guide by Alan Graham, Hodder and Stoughton, London, 1990, ISBN 0 340 4931 1 9. This is a more thorough introduction to dealing with data and statistics. Statistics without tears, by Derek Rowntree, Penguin, Harmondsworth, 1981, ISBN 0 14 013632 0 is intended to support those people without a previous background in statistics, who may need it as part of a course that they are studying. Finally, all the topics are comprehensively covered in the Open University course MU 120 Open Mathematics. This course assumes you are already reasonably confident with the material covered by any of the books marked () or by Module 1 of Countdown to mathematics Volume 1. The course has been studied successfully by many students whose primary interest lies in the humanities or social sciences.
9781885767 Logic: Student (1st edition) Covering topics in logic too often reserved for a college course, Intermediate Logic simplifies various elements of propositional and symbolic logic, including truth tables and formal proofs of validity. While this textbook/workbook can be used for one year's worth of study, older students may work through Introductory Logic and Intermediate Logic in a school year. Recommended for grades 8 and up. 20 lessons/35
Franklin Park, IL Geometry just adding and multiplication but computing eignevalues, too, or the Gauss elimination. In other classes, as Crystallography or Statics, it was mainly 3-D vectors. In a computer science class, we used the MatLab to operate with matrices.?s understanding
t... read more An Introduction to the Theory of Linear Spaces by Georgi E. Shilov, Richard A. Silverman Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition. An Introduction to Orthogonal Polynomials by Theodore S Chihara Concise introduction covers general elementary theory, including the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula, special functions, and some specific systems. 1978 edition. The Laplace Transform by David V. Widder This volume focuses on the Laplace and Stieltjes transforms, offering a highly theoretical treatment. Topics include fundamental formulas, the moment problem, monotonic functions, and Tauberian theorems. 1941 edition. Complex Analysis with Applications by Richard A. Silverman The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index. Complex Analysis in Banach Spaces by Jorge Mujica The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. 1986 edition. Sets, Sequences and Mappings: The Basic Concepts of Analysis by Kenneth Anderson, Dick Wick Hall This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition. Product Description: the real number system, the text presents results for subsets and functions related to Euclidean space of n dimensions. It offers a rigorous review of the fundamentals of calculus, emphasizing power series expansions and introducing the theory of complex-analytic functions. Subsequent chapters cover sequences of functions, normed linear spaces, and the Lebesgue interval. They discuss most of the basic properties of integral and measure, including a brief look at orthogonal expansions. A chapter on differentiable mappings concludes the text, addressing implicit and inverse function theorems and the change of variable theorem. Exercises appear throughout the book, and extensive supplementary material includes a bibliography, list of symbols, index, and appendix with background in elementary set theory
self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities. less
Generally scheduled 10-39 hours each week. Ability to apply basic mathematical concept Generally scheduled 10-39 hours each wee
2ndMore About This Textbook Overview Work more effectively and gauge your progress along the way! This Student Study Guide is designed to accompany Hughes-Hallett's Applied Calculus, 2nd Edition. It is a step-by-step guide that walks students through the text as they read it and work problems while supporting the discovery approach. Achieving a fine balance between the concepts and procedures of calculus, Applied Calculus, 2nd Edition provides readers with the solid background they need in the subject with a thorough understanding of its applications in a wide range of fields - from biology to economics. Related Subjects Table of Contents Functions and Change. Rate of Change: The Derivative. Accumulated Change: The Definite Integral. Short-Cuts to Differentiation. Using the Derivative. Using the Integral. Functions of Several Variables. Differential Equations. Appendix. Answers to Odd Numbered Problems
Book summary One of the most important tasks in finance is to find good mathematical models for financial products, in particular derivatives. However, the more realistic the model, the more practitioners face still-unsolved problems in rigorous mathematics and econometrics, in addition to serious numerical difficulties. The idea behind this book is to use Mathematica® to provide a wide range of exact benchmark models against which inexact models can be tested and verified. In so doing, the author is able to explain when models and numerical schemes can be relied on, and when they can't. Benchmarking is also applied to Monte Carlo simulations. Mathematica's graphical and animation capabilities are exploited to show how a model's characteristics can be visualized in two and three dimensions. The models described are all available on an accompanying CD that runs on most Windows, Unix and Macintosh platforms; to be able fully to use the software, Mathematica 3 is required, although certain features are usable with Mathematica 2.2. This product will prove of inestimable worth for financial instrument valuation and hedging, checking existing models and for analyzing derivatives; it can be used for professional or training purposes in financial institutions or universities, and in MBA courses. [via]
Reviewing Mathematics : Preparing for the Eighth-Grade Test To prepare students for the New York Eighth-Grade Test beginning in March 2006. This book provides a complete review of the four strands tested on the New York Eighth-Grade exam: Number Sense & Operations, Algebra, Geometry, and Measurement
AISCT Upper School Curriculum (Grades 7-12) (revised April 2005) Page 1 of 3 Subject Grade(s) Topic Objectives/Skills Algebra II 10 The learner will… Algebra solve equations and inequalities involving absolute value solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices are adept at operations on polynomials, including long division factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically plot complex numbers as points in the plane add, subtract, multiply, and divide complex numbers add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula apply these techniques in solving word problems solve quadratic equations in the complex number system demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+ c graph quadratic functions and determine the maxima, minima, and zeros of the function know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay determine whether a specific algebraic statement involving rational expressions, radical expressions, or exponential functions is sometimes true, always true, or never true apply the method of mathematical induction to prove general statements about the positive integers find the general term and the sums of arithmetic series and of both finite and infinite geometric series derive the summation formulas for arithmetic series and for both finite and infinite geometric series AISCT Upper School Curriculum (Grades 7-12) (revised April 2005) Page 2 of 3 Subject Grade(s) Topic Objectives/Skills Algebra II 10 The learner will… Algebra solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions use properties from number systems to justify steps in combining and simplifying functions perform addition and subtraction on matrices multiply matrices by a scalar and perform matrix multiplication demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations know that a square matrix is invertible if, and only if, its determinant is nonzero compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule The learner will… use fundamental counting principles to compute combinations and permutations use combinations and permutations to compute probabilities know the binomial theorem and use it to expand binomial expressions that are raised to Statistics, Data positive integer powers know the definition of the notion of independent events and can use the rules for addition, analysis, and multiplication, and complementation to solve for probabilities of particular events in finite Probability sample spaces know the definition of conditional probability and use it to solve for probabilities in finite sample spaces demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses be familiar with the standard distributions (normal and binomial) and can use them to solve for events in problems in which the distribution belongs to those families determine the mean of a normally distributed random variable organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events AISCT Upper School Curriculum (Grades 7-12) (revised April 2005) Page 3 of 3 Subject Grade(s) Topic Objectives/Skills 10 Algebra II know the definition of conditional probability and use it to solve for probabilities in finite sample spaces understand the notion of a continuous random variable and can interpret the probability of an outcome as the area of a region under the graph of the probability density function Statistics, Data associated with the random variable know the definition of the mean of a discrete random variable and can determine the mean analysis, and for a particular discrete random variable Probability cont. know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations be familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error determine the P-value for a statistic for a simple random sample from a normal distribution
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
This Student Reference Book can be used to look up and review topics in mathematics. It has the following sections: 1) A Table of Contents that lists the sections and shows how the book is organized. 2) Essays within each section. 3) Directions on how to play some of the mathematical games you may have played before. 4) A Data Bank with posters, maps, and other information. 5) A Glossary of mathematical terms. 6) An Answer Key and 7) An Index to help you locate information quickly.
Introduction to Algebra, Linear Equations and Inequalities, Graphing Equations, Systems of Linear Equations In Two Variables, Polynomials and Exponents, Factoring Polynomials and Solving Equations, Rational Expressions, Radical Expressions, Quadratic Equations MARKET: For all readers interested in algebra. ...show less
Mathematics \| Mathematics A language arts guided reading literacy book, this title is part of the iOpeners reading series and is appropriate for grade five readers. Each chapter takes a close look at a different type of survey, from Nielsen television ratings to election polling surveys. Williams' formulae, factors and accurate shorts were first used to help his students, but then the author saw that many professional construction workers also could not make simple calculations in the field. )-- Author, teacher and contractor Kenneth Williams, Sr., announced today the release of...
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
Scope and Content: Judging from binding, paper and handwriting, these mathematical practice books probably date from the late 18th to mid-19th centuries. The first concentrates on principles of accountancy and includes simple and compound interest, discounts, barter, loss & gain, fellowship or joint stock, and foreign and domestic exchange rates—all with practical applications and exercises. The second book appears to have been used by several pupils. Names that appear within the pages and on the back end sheet are: Miss Emma Harrison, Miss Lucy S. Harrison Tenth Legion, Rockingham County, Va., William C. Harrison, and Mr. John Harrison with the date, March 1, 1853. One math problem cites the date, May 17, 1781 while a handwritten note tucked into the pages is inscribed with an invitation to a picnic and cotillion on May 20, 1869 at the residence of A. B. Bowman on Smith Creek. The names Bettie A. and David W. Harrison of Tenth Legion are written several times on the reverse. The books are decidedly American and specifically, Virginian as several examples indicate starting points as Baltimore, Philadelphia and an ending point at Richmond. Weights and measures, however, are given in English, Federal, and even Virginia currency. Subjects covered include: simple and compound addition, multiplication, long division, proportions, and integers. Practical applications include conversions from one measure or distance to another and calculating payments for mercer's, draper's, grocer's, and milliner's bills among others.
Precalculus - 3rd edition effectiveness to not only pass the course, but truly understa...show morend the material. Features Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses. Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation. Zeros, Solutions, and x-Intercepts Theme: This theme allows students to reach a new level of mathematical comprehension through connecting the concepts of the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function. Technology Connection: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems. Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section. Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation. Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together. Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.'' Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics. Classify the Function: With a focus on conceptual understanding, students are asked to identify a number of functions by their type (i. e., linear, quadratic, rational, and so forth). As students progress through the text, the variety of functions they know increases and these exercises become more challenging. These exercises appear with the review exercises in the Skill Maintenance portion of an exercise setGood Books Will Follow Kansas City, MO 2007 Hardcover Fair Minor shelf / edge wearInstructor's Edition48 +$3.99 s/h VeryGood Penntext Downingtown, PA Excellent Condition. No wear/tear. Please contact us if you have any Questions321460065
algebra The definition of algebra is a type of math that focuses on demonstrating the properties and relationships of abstract things in symbolic form. Graphing, absolute value equations and scientific notation are each an example of a topic in algebra. Examples of algebra on a chalkboard. algebra definition by Webster's New World noun a mathematical system using symbols, esp. letters, to generalize certain arithmetic operations and relationships (Ex.: x + y = x represents a unique relationship between x and y, and has an infinite number of examples, as 3 + 6 = 9) algebra definition by American Heritage Dictionary noun A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.
Let "Geometry Pro" serve as your portable tutor. This application contains a rich collection of examples, tutorials and solvers, crafted by a professional math tutor with over 20 years of applied mathematics and teaching experience. This application covers:Check the Android Market for more video Geometry tutorials from iPREPpress. * The VIDEOS in this app are resident, not streamed from the Internet. You can use this product anywhere. Designed especially for teen audiences, graphics, animation, live-action whiteboard and voice audio make the presentations engaging. The instructors are experts in their field and make the material easy to understand. Each audio and video tutorial app has been meticulously created by iPREPpress LLC, a leader in educational iPod, iPhone, iPad, Android and mobile device development and distribution. More from developer The application contains all basic calculators aimed to evaluate volume of different geometric figures. Users can find illustrations with standard designations and formulas. The volume frequently can be calculated by using different formulas. This aspect is also embodied in the application. Calculators are available both in Russian and in English! This package is helpful mostly for school and university students, who study geometry fundamentals. There are following calculators in application: • Volume of Cylinder • Volume of Cube • Volume of Parallelepiped • Volume of Pyramid • Volume of Sphere • Volume of Cone • Volume of Prism • Volume of Tetrahedron • Volume of Truncated Pyramid • Volume of Truncated Cone Advantages: - Visual and clear calculators as they contain vivid illustrations and formulas. - Calculators contain all possible formulas to evaluate volume The application contains all basic calculators aimed to evaluate area of different geometric figures. Users find illustrations with standard designations and formulas. Area frequently can be calculated by using different formulas. This aspect is also embodied in the application. Calculators are available both in Russian and in English! This package is helpful mostly for school and university students, who study geometry fundamentals. Calculators of planar figures: • Area of Triangle • Area of Circle • Area of Rectangle • Area of Trapezoid • Area of Square • Area of Parallelogram • Area of Rhombus • Area of Ring • Area of Circle Sector • Area of Ellipse • Area of Circle Segment Calculators of three-dimensional figures: • Area of Pyramid • Area of Cube • Area of Parallelepiped • Area of Sphere • Area of Cone • Area of Truncated Cone • Area of Cylinder Advantages: - Visual and clear calculators as they contain vivid illustrations and formulas. - Calculators contain all possible formulas to evaluate area
The most helpful favorable review The most helpful critical review 23 of 23 people found the following review helpful 5.0 out of 5 starsPhenomenal resource for math competition coaches and students... 3.0 out of 5 starsSomewhat Disappointed... would find in a Math Counts or AMC contest. You will learn some new tricks (they were new to me at least) that helps solve problems much more quickly. I recommend it to new coaches who have caught the math competition bug but don't know where to get materials, or even experienced coaches who want another outstanding resource for their library. For someone still trying to learn all of the ins and outs of middle school math contests, this has vaulted into a spot as one of my go-to resources, along with the Art of Problem Solving series and old Math Counts problems. This is an impressive collection of competition math problems that are explained very well! The book addresses multiple levels of ability and is a wonderful source of interesting mathematics. As a high school math coach of many years I can say that this book is NOT just for Middle School! It's a great high school math book. Math teachers everywhere need to be challenging students to think. "Competition Math for Middle School" is just what they need. I recommend this book to math teachers teaching everything from Algebra 1 to Calculus. Topics in the book include Number Theory, Geometry and Combinatorics. It's a treat! We bought this for my son to help him study for the Math Counts competition - and just as a resource to supplement his math curriculum. He loved the book and found it VERY helpful. Would highly recommend it. I use this book as a supplement to my daughter's school math. I like this book because it explains how simple mathematical concepts can be applied in competition level. This book provides with many practice questions that students can practice until they get familiar with similar questions. My daughter is smart but sometimes, can be scared of these competition math questions. This book is not too difficult that both average and smart students can learn from it. The explanation is simple but comprehensive. This book is not filled with those arrogant questions that can make kids feel defeatism in math. I gave the questions in the probability section to my daughter after she learned probability at the school. She learned how school math can be expanded and applied to the competition level from this book. Not all kids who are interested in math are genius. This book is for those students. I highly recommend this book. I'm doing Mathcounts in my school, and wanted some resources to help me perform better in the chapter and state competitions. I was on and online course at artofproblemsolving.com for advanced Mathcounts/AMC 8, and in the previous years I had taken a course on Johns Hopkins CTY. I bought this book on Artofproblemsolving.com because it was meant for contest "mathletes" like me. Instantly, I focused areas on my weak sections of math, like probability/counting, and geometry. I reviewed the probability section for a few days and in what seems like an instant, it became my best subject. This book teaches the reader through the concepts first, with a few worked examples, then lets you do it on your own. The problems are challenging, fun, and serve as an excellent resource for sharpening skills on weak areas. Now, I'm working on the geometry section. Also, this book shows slick methods for hard problems, like "How many different rectangles can be formed on an 8x8 chessboard?" Overall, I think this is an excellent resource for one who is serious about competition math and wants to excel in competitions like mathcounts. A last thing I would recommend is that people who want to buy this book is that they should be somewhat confident that they will proceed to state mathcounts(or at least, have some experience). have learnt not to spend too much time on certain problems or sections that are not properly sized. I am in my Math Counts team in Middle School and this was a great book. It talked about a lot of interesting math-related topics. All of my team mates had gotten this book, so I decided to buy it too and it was a good decision. I will recommend this book to everyone who needs some math competition help in middle school. This is a very good book for middle schoolers who are looking to learn more math and want to be challenged. This is my son's first math book - other than his school text books. The concepts are taught by working through the example problems. The problems in the book are generally tougher and more advanced than the ones in the middle school text books. He finished the book this summer and he loved working through the problems on his own. Kids need to be challenged and taught to think on their own. This book helped him do that. Love the book. Good examples and plenty of practice. We are not into competition Math. We only bought this book to challenge my son who is very good at Math, we use it as "daily challenge problem." The questions are not boring, explanations are very well worded. My son has a lot of fun with it. I suggest that you purchase this at Algebra level. We are doing pre-algebra, so it's still a bit hard, but manageable only because my son loves Math. Apparently there is a 50 percent attrition rate for American students taking their first college calculus course. Considering that a lot of these students didn't get into these schools by being underqualified, what is the problem? Who are the ones who succeed? It seems the absence of real mathematical problem solving as a regular feature of a middle school and high school curriculum is contributing to the problem mentioned. The reasons such programs are not common appear a mix of culture and politics and sadly it misleads students tremendously. Differently, experience with problem solving seems to contribute much to those who truly understand mathematics as an activity and consequently succeed in the undergraduate setting and beyond. If one would like to fill this void somehow, Batterson's book is an excellent segway into higher mathematics. Maybe the title is a good marketing device, but a misnomer nonetheless -- it could be called a "Problem Solving Primer." Olympiad books require a great deal of sophistication that even a relatively successful undergraduate student might lack. Batterson, perhaps augmented with Polya, is the place to cut your teeth initially, and the transition beyond will seem more seemless.
Maple includes more than 5,000 mathematical functions and a variety of options for high-performance computing. Maple 16 makes available new techniques and tools in the Clickable Math collection, such as "drag-to-solve" and "smart popups." Drag-to-solve allows users to tackle problems by dragging terms to the desired location and save each step in the calculation. Smart popups let users adjust a single part of a highlighted calculation and preview the answer. It also notifies the user which mathematical identities can be used, if a subexpression can be factored, and shows the plot. "Teaching Calculus with Maple: A Complete Kit" was developed over five years by Jack Weiner, professor emeritus of mathematics at University of Guelph in Ontario, Canada. The kit has been field- tested in classrooms with 15 to 600 students. Notes for the teachers with annotation and demonstrations using Maple; Automatically graded homework assignments for Maple T.A. users, including feedback and hints, as well as assignments for users who don't have access to Maple T.A.; and Extra homework assignments from Stewart's Calculus. "Using Maple as the foundation of each lecture has resulted in fun, extremely interactive classes. We're reaching more students now than ever before," said Weiner. "In addition, the use of Maple T.A. to reinforce learning by providing lots of practice and immediate feedback gives students more confidence, which ultimately leads to greater success." "Teaching Calculus with Maple: A Complete Kit" is free for schools that use Maple or Maple T.A
Product description Algebra 1/2 represents a culminatin of prealgebra mathematics, covering all topics normally taught in prealgebra, as well as additional topics from geometry and discrete mathematics. This program is recommended for seventh graders who plan to take first-year algebra in the eighth grade or for eighth-graders who plan to take first-year algebra in the ninth grade. Type: Boxed Set ()Category: > Home SchoolingISBN / UPC: 9781565774995/156577499XPublish Date: 1/1/2002Item No: 107062Vendor: Saxon Publishers
Marcos, machine learning is still very young, and in a state of great flux. What this means is that the techniques used are constantly developing, and if you looked across the whole spectrum, you'd see a dizzying variety of methods. What I recommend is to google around for courses on topics you are interested in, both at the school you will attend and at others you respect, and see what the textbooks, notes, and homework assignments look like. – Matus TelgarskyJan 15 '10 at 10:15 2 Answers For basic neural networks (i.e. if you just need to build and train one), I think basic calculus is sufficient, maybe things like gradient descent and more advanced optimization algorithms. For more advanced topics in NNs (convergence analysis, links between NNs and SVMs, etc.), somewhat more advanced calculus may be needed. Since you are a biologist, I don't know whether you studied linear algebra. Some basic ideas from there are definitely extremely useful. Specifically, linear transformations, diagonalization, SVD (that's related to PCA, which is a pretty basic method for dimensionality reduction). The book by Duda/Hart/Stork has several appendices which describe the basic math needed to understand the rest of the book.
This standard text, written for junior and senior undergraduates, is unusual in that its presentation is accessible enough for the beginner, yet its thoroughness and mathematical rigor provide the more advanced student with an exceptionally comprehensive treatment of every aspect of modern algebra... read more Abstract Algebra by W. E. Deskins Excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. Features many examples and problemsThe Algebraic Structure of Group Rings by Donald S. Passman "Highly recommended" (Bulletin of the London Mathematical Society) and "encyclopedic and lucid" (Bulletin of the American Mathematical Society), this book offers a comprehensive, self-contained treatment of group rings. 1985Boolean Algebra by R. L. Goodstein This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions. Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems. Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are providedLinear Algebra by Georgi E. Shilov Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, and more. Product Description: This standard text, written for junior and senior undergraduates, is unusual in that its presentation is accessible enough for the beginner, yet its thoroughness and mathematical rigor provide the more advanced student with an exceptionally comprehensive treatment of every aspect of modern algebra. It especially lends itself to use by beginning graduate students unprepared in modern algebra. The presentation opens with a study of algebraic structures in general; the first part then carries the development from natural numbers through rings and fields, vector spaces, and polynomials. The second part (originally published as a separate volume) is made up of five chapters on the real and complex number fields, algebraic extensions of fields, linear operations, inner product spaces, and the axiom of choice. For the benefit of the beginner who can best absorb the principles of algebra by solving problems, the author has provided over 1300 carefully selected exercises. "There is a vast amount of material in these books and a great deal is either new or presented in a new form." — Mathematical Reviews. Preface. List of Symbols. Exercises. Index. 28 black-and-white line
Perrine, FL Calculus and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations...
Beginning Algebra With Applications 9780618803590 ISBN: 0618803599 Pub Date: 2007 Publisher: Houghton Mifflin Summary: Intended for developmental math courses in beginning imm...ediate feedback, reinforcing the concept, identifying problem areas, and, overall, promoting student success."New!" "Interactive Exercises" appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles."New!" "Think About It" Exercises are conceptual in nature and appear near the end of an objective's exercise set. They ask the students to think about the objective's concepts, make generalizations, and apply them to more abstract problems. The focus is on mental mathematics, not calculation or computation, and help students synthesize concepts."New!" "Important Points" have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently."New!" A Concepts of Geometry section has been added to Chapter 1."New!" Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction"New!" A Complex Numbers section has been added to Chapter 11, "Quadratic Equations.""New Media!" Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool. Aufmann, Richard N. is the author of Beginning Algebra With Applications, published 2007 under ISBN 9780618803590 and 0618803599. Four hundred three Beginning Algebra With Applications textbooks are available for sale on ValoreBooks.com, one hundred twenty nine used from the cheapest price of $23.67, or buy new starting at $65.91.[read more] Ships From:Multiple LocationsShipping:Standard, ExpeditedComments:RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). FREE TRACKING/DELIVERY CONFIRMATION ON ALL ORDERS! ! A used book that may have some cosmetic wear... [more]RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks).i1 i1
Mathematics 130, Precalculus Mathematics II, is the second of a two-semester sequence that provides the background for students who are preparing to take calculus. Topics include graphing, systems of equations, matrices, complex numbers, mathematical induction, the binomial theorem, sequences and series, polar coordinates, parametric equations, trigonometric functions, inverse trigonometric functions, law of sines, law of cosines, and trigonometric identities. Prerequisites: MATH 129 or equivalent or consent of department. A graphing calculator is required. i. In writing, using everyday mathematical language, including symbols. ii. Orally, using both everyday and mathematical language. c. Programs prepare prospective teachers who can make and evaluate mathematical conjectures and arguments and validate their own mathematical thinking. d. Programs prepare prospective teachers whoˇ i. Show an understanding of the interrelationships within mathematics. ii. Connect mathematics to other disciplines and real-world situations. e. Programs prepare prospective teachers whoˇ i. Use calculators in computational and problem-solving situations. ii. Use computer software to explore and solve mathematical problems. 11. TEACHER PREPARATION 2.1 Programs prepare prospective teachers who can identify and model strategies used for problem-solving in grades 7-12. a. Programs prepare prospective teachers who use graphing calculators, computers and other technologies as tools for teaching mathematics. VI.EVALUATION CRITERIA/GRADING SC Partial credit for problems is awarded on the basis of work shown. Homework will be collected randomly at a rate averaging about once a week and given a grade of either pass or fail. Only a few homework problems will be graded but all problems must be attempted and all work must be shown. The homework score will depend on the percentage of passing grades assigned for collected assignments. Late homeworks will not be accepted and the final exam grade will be used as the grade for all tests that are missed. Make up tests will not be given. The lowest score for an in class test can be replaced with the Final Exam grade (if it helps) and the class test average will be computed as in the example below. The percentage of passing homework grades will be multiplied by four, rounded, and the result added to the final average. Example: To see how your grade will be calculated, suppose your test scores are 85, 81, 84, and 90, your final exam score is 88 and you received a passing grade on 50% of the homework collected. Since the lowest test grade is dropped (see item 1 under COURSE REQUIREMENTS), your grade would be calculated as followsVII.COURSE OUTLINE See attached calendar. * Subject to change by myself for the optimization of instructional assistance. VIII.TEACHING STRATEGIES Math 130 is a lecture-based course. Each lecture will contain a summary of the most important concepts from each chapter. The graphing calculator will be utilized to bring clarity and understanding to each concept or theory discussed. Questions will be posed to the class daily to measure their comprehension of particular concepts. IX.COURSE REQUIREMENTS Conduct of Course/Classroom Decorum 1. Students are responsible for availing themselves of all class meetings, Tutorial sessions, computer lab sessions, and individual help from the instructor. There are computer software tutorials available for your use in the Helen Chick Building, second floor and SBE 216A. (See the Lab Assistants) 2. Students are responsible for maintaining a notebook of problems selected by the instructor. Students are encouraged to include as many additional problems as is possible 3. All tests will be announced prior to their administration. Since the lowest test will be dropped no make-up test will be given. There will be a test given at the end of each chapter and there will be a comprehensive final examination given. The students are also required to take the algebra profile posttest. 4. Students are expected to enter the classroom on time and remain until the class ends. Late arrivals and early departures will be noted in the record book. The class attendance policy set forth in the 1996-1998 FSU Catalogue will be strictly adhered to. 5. Students must refrain from smoking, eating, and drinking in the classroom. The rights of others must be respected at all times and to spend adequate time on their class work and to read each topic prior to class discussion to insure that the course objectives are met. Two hours of home study is expected for each hour of class. 8. Talking in class between students is strictly unacceptable. Discussions should be directed to the instructor. 9. Extra recitation periods and/or computer lab attendance are mandatory for students whose grades fall below C. They must meet the instructor to arrange for extra activities. 10. Dishonesty on graded assignments will not be tolerated. Students must neither give nor receive help on any work to be graded. The University policy on cheating will be applied to any violations. The minimum penalty will be a grade of zero on the assignment.
Intended Outcomes for the course Upon successful completion students should be able to: , €¢ Analyze real world scenarios to recognize when trigonometric functions, vector arithmetic, the polar coordinate system, or parametric equations are ,appropriate, formulate problems about the scenarios, creatively model these scenarios (using technology, if appropriate) in order to solve the problems using multiple approaches, judge if the results are reasonable, and then interpret and clearly communicate the results. ,€¢ Appreciate trigonometric, parametric, and vector concepts that are encountered in the real world, understand and be able to communicate the ,underlying mathematics involved to help another person gain insight into the situation. ,€¢ Work with trigonometric functions, vector arithmetic, the polar coordinate system, and parametric equations in various situations and use correct mathematical terminology, notation, and symbolic processes in order to be prepared for future coursework in calculus and the sciences that requires the use of and an understanding of the concepts of elementary functions. Course Activities and Design All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. In-class time is primarily activity/discussion emphasizing problem solving techniques. Activities will include group work. Outcome Assessment Strategies Assessment shall include: , 1. The following must be assessed in a proctored, closed-book, no-note, and no-calculator setting: finding the exact values of the trigonometric functions at integer multiples of 0, π/6, π/4, π/3, π/2and π, using the Pythagorean identities, and using the relationships between the six trigonometric functions. , 2. At least two proctored, closed-book, no student-notes (an instructor-provided list of identities and formulas is allowed; see Addendum B) exams, one of which is a comprehensive final exam that is worth at least 25% of the overall grade. The proctored exams should be worth at least 60% of the overall grade. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate. , 3. Various opportunities to express €" and be graded on €" mathematical concepts in writing. Assessment should be made on the basis of using correct mathematical syntax, appropriate use of the English language, and explanation of the mathematical concept. , 4. At least two of the following additional measures: , a. Take-home examinations , b. Graded homework , c. Quizzes , d. Group projects , e. In-class activities , f. Portfolios , g. Individual projects , 5. Additional forms of assessment that do not have to be part of the grade: (see math department web resource for additional strategies) , a. Attendance , b. Individual student conference , c. In-class participation Course Content (Themes, Concepts, Issues and Skills) 1.0 Angles , Develop an understanding of angles in different systems of measure. , 1.1 Understand the definition of an angle in standard position and identify the initial and terminal rays. , 1.2 Express the measure of an angle in degrees, degrees-minutes-seconds (DMS), and radians. , 1.2.1 Convert between the angle-measures listed in 1.2. , 1.3 Sketch an angle of any given measure in standard position and identify the related or reference angle and coterminal angles. , 1.4 Find the length of an arc on the circumference of a circle using the definition of an angle in radian measure. , 2.0 PERIODIC FUNCTONS , Explore and analyze periodic functions. , 2.1 Determine if a function is periodic. , 2.2 Determine the period of a periodic function. , 2.3 Determine the amplitude and midline of a periodic function where applicable. , 2.4 Define the sine and cosine functions in terms of the unit circle. , 2.5 Determine the period, midline, and amplitude of the sine and cosine functions. , 2.6 Define the tangent function in terms of the sine and cosine functions and determine its period. , 2.7 Define the reciprocal trigonometric functions. , 3.0 RIGHT TRIANGLE TRIGONOMETRY , Develop an understanding of right triangle trigonometry using both radians and degrees. , 3.1 Define the six trigonometric functions of an acute angle in terms of the sides of a right triangle. , 3.2 Solve right triangles given two sides or a side and a non-right angle of the triangle. , 3.3 Evaluate the exact values of the six trigonometric functions using and triangles. All work in this course will be evaluated for your ability to meet the following writing objectives as well as for "mathematical content." , 1. Every solution must be written in such a way that the question that was asked is clear simply by reading the submitted solution. , 2. Any table or graph that appears in the original problem must also appear somewhere in your solution. , 3. All graphs that appear in your solution must contain axis names and scales. All graphs must be accompanied by a figure number and caption. When the graph is referenced in your written work, the reference must be by figure number. Additionally, graphs for applied problems must have units on each axis and the explicit meaning of each axis must be self-apparent either by the axis names or by the figure caption. , 4. All tables that appear in your solution must have well defined column headings as well as an assigned table number accompanied by a brief caption (description). When the table is referenced in your written work, the reference must be by table number. , 5. A brief introduction to the problem is almost always appropriate. , 6. In applied problems, all variables and constants must be defined. , 7. If you used the graph or table feature of your calculator in the problem solving process, you must include the graph or table in your written solution. , 8. If you used some other non-trivial feature of your calculator (e.g., SOLVER), you must state this in your solution. , 9. All (relevant) information given in the problem must be stated somewhere in your solution. , 10. A sentence that orients the reader to the purpose of the mathematics should usually precede symbol pushing. , 11. Your conclusion shall not be encased in a box, but rather stated at the end of your solution in complete sentence form. , 12. Line up your equal signs vertically. , 13. If work is word-processed all mathematical symbols must be generated with a math equation editor.
Elements of Partial Differential Equations [NOOK Book] Overview Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems... More About This Book Overview Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory. Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent study will particularly appreciate the worked examples that
In this paper, published in the 1988 book The teaching and assessing of mathematical problem solving, Lauren Resnick of the University of Pittsburgh proposes using everyday language in the classroom, so that students can gain a more conceptual, coherent, and meaningful understanding of mathematics. A geometry.pre-college newsgroup discussion.
Niantic, PA CalculusThe outline of all the areas of math and science is punctuated by rules derived from theoretic understanding of that subject. Similarly, as in a spoken or written language the sciences and mathematics have their rules connecting the theory. To become fluent, the rules must be mastered by each student studying that subject
За всички, които мислят, че не обичат математиката This is a great book for those who think they don't like mathematics. This book includes: Mathematical Ways of Thinking; Number Sequences; Functions and Their Graphs; Large Numbers and Logarithms; Symmetry and Regular Figures; Mathematical Curves; Methods of Counting; The Mathematics of Chance; An Introduction to Statistics; and Topics in Topology. Hardcover, 382 pages Published 1983 by Наука и изкуство (first published February 8th 1971) Community Reviews There is more to mathematics than computational techniques! Jacobs' clear and entertaining text (which is full of cartoons, pictures, and anecdotes) inspires a love of math. Each chapter invites the reader to discover for himself the patterns and structure of a particular topic. This book helped to convert me into someone who appreciated mathematics. I love this math text! It happens to be one of my favorite books of all time. You know, I didn't even like mathematics before I started teaching. Funny then, that after five years of doing so I would find a text book that intrigued me so much that it would become a highly prized object.
Intended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory ...Show synopsisIntended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory in small steps and provides more examples and exercises involving computations than competing texts
Dorling Kindersley Teaching Pro: Advanced Math delivers comprehensive coverage of the complete high school math curriculum with tips, tricks and secrets that will help you make sense of teachers and textbooks! Each interactive strategic lesson supports state standards and follows grade-based curriculum using self-paced learning and stress-free quizzes to build your math knowledge and test-taking skills. An ultimate skill-building resource with full subject, comprehensive learning.
Intended for those students majoring in Mathematics Education. This class presents historical topics that teachers can use in their math classrooms. This course introduces mathematical ideas and problem-solving strategies that have evolved from ancient times to the present. TAUGHT: Winter CONTENT AND TOPICS: The course will begin with computing techniques used in antiquity and how they have come to influence present day methods. Students will solve quadratic equations and verify algebraic identities using geometric methods developed by Thales and Pythagoras. The Geometry of Euclid will be discussed with special emphasis on how his theory of parallels would centuries later motivate the advent of non-Euclidean Geometries. Problems will be investigated that will establish a distinct contrast between Greek and Hindu Mathematics. The invention of the Calculus in the seventeenth centry will be studied with special attention given to those mathematical results that paved the way for this "new" mathematics that would forever change the modern world. The course will conclude with an investigation into nineteenth and twentieth century mathematics. Emphasis will center on Cantor's set theory, with special attention given to his Axiom of Choice and the turmoil this axiom created in early twenthieth century mathematics. Topology, Logic and David Hilbert's Formalism will be addressed as time allows. GOALS AND OBJECTIVES: 1. Gain an appreciation for great mathematicians throughout history, their work and in some cases great sacrifice. 2. Gain an understanding of how mathematics developed and some of the different processes it went through in the development. 3. Gain an understanding of the importance of symbols in mathematics, why they are important, and how they develop. 4. Learn how mathematics was used through the ages by men both to help mankind and for purposes such as war and how differences in mathematics affected culture. REQUIREMENTS: Each student must have the textbook selected for the course. Assignments will consist of reading from the textbook, working certain mathematical problems listed at the end of the reading sections, and quizzes over the reading and math problems assigned. There will be chapter tests to assess material covered in the textbook. There will be outside reading assignments that supplement the textbook, written assignments relating to individual research, and oral reports. PREREQUISITES: Math 113 or concurrent enrollment in Math 113 and the consent of the instructor.
Designed for elementary school teachers. A constructive development of the real number system beginning with the system of whole numbers; concepts from elementary number theory; applications of quantitative systems to problems in discrete mathematics. Prerequisite: High school algebra and geometry. Offered: every semester
KSOM is conducting a refresher course during April 2014 for B.Sc. Mathematics students, doing their second year and studying in colleges in Kerala. The main objectives of AFS are to bring up students with diverse background to a common level and help them acquire basic knowledge in algebra, analysis and topology. This programme is organised by National Centre for Mathematics (NCM). The school will start with a review of the theory of classical modular forms in one variable, as background for the advanced courses to follow on Mock theta functions, Mock modular forms and their application. WELCOME TO KSOM Kerala School of Mathematics (KSOM), an institution meant for advanced learning and research in Mathematics, is a joint venture of Kerala State Council for Science, Technology and Environment (KSCSTE), Government of Kerala and Department of Atomic Energy (DAE), Government of India. More> KSOM is conducting a refresher course during April 2014 for B.Sc. Mathematics students, doing their second year and studying in colleges in Kerala. The course will cover some basic topics of Algebra, Analysis, Linear Algebra and Number Theory. Registration open - Last Date: 30-03-2014 The main objectives of AFS are to bring up students with diverse background to a common level and help them acquire basic knowledge in algebra, analysis and topology. This programme is organised by National Centre for Mathematics (NCM). Selected Applicants. The school will start with a review of the theory of classical modular forms in one variable, as background for the advanced courses to follow on Mock theta functions, Mock modular forms and their application.
Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved... more... This fourth edition offers a comprehensive overview of advanced calculus in a highly readable format. The book offers substantial coverage of vector and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometric and physical significance of mathematical relations. Numerical methods are touched on at various points because of their practical value and the insights... more... Packed with practical examples, graphs, and Q&As, this complete self-teaching guide from the best-selling author of Algebra Demystified covers all the essential topics, including: absolute value, nonlinear inequalities, functions and their graphs, inverses, proportion and ratio, and much more. This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ample examples and brief explanations---with very few proofs and little axiomatic machinery---are used to highlight all the major results of real analysis, from the basics of sequences and series to the more advanced concepts of Taylor and Fourier series,... more... This text for advanced undergraduates and graduates reading applied mathematics, electrical, mechanical, or control engineering, employs block diagram notation to highlight comparable features of linear differential and difference equations, a unique feature found in no other book. The treatment of transform theory (Laplace transforms and z-transforms) encourages readers to think in terms of transfer functions, i.e.... more... David Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the... more... The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued... more... This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable
Mathematics Applied to Electronics - 6th edition Summary: For undergraduate college-level courses in Mathematics for Electronics, Tech Math (Algebra and Trigonometry) for Electronics, Computer, Automation, and Electromechanics. This text provides an introduction to mathematics applied to electronics, computers, electromechanics, and automation. Organized to be compatible with electric circuit books currently in use, its content balances a formal proof-orientation against the need for expediency in developing a br...show moreoad, general mathematics ability. Features NEW--Companion website at multiple choice and true/false review quizzes for each chapter. Tests the students comprehension and e-mails the score back to the instructor. Natural Numbers and Number Systems. Signed Numbers. Numerical Expressions and Equations. Order of Operations. Symbols of Grouping. Double Meaning of + and -. Absolute Value of a Signed Number. Combining Signed Numbers. Relational Operators. Multiplying with Signed Numbers. Dividing with Signed Numbers. International System of Units. Selected Physical Quantities. Forming Decimal Multiples and Submultiples of the SI Units. Unit Analysis and Conversion between Systems. Applying Unit Analysis to Energy Cost. Units and Exponents. Multiplying Monomials. Multiplying a Monomial and a Binomial. Multiplying a Monomial and a Polynomial. Subtracting Polynomials. Additional Work with Polynomials. Division of Monomials. Dividing a Polynomial by a Monomial. Factoring Polynomials with a Common Monomial Factor. Evaluating Algebraic Expressions. Voltage Division in a Series Circuit. Conductance of the Parallel Circuit. Equivalent Resistance of the Parallel Circuit. Current Division in the Parallel Circuit. Solving Parallel Circuit Problems. Using Network Theorems to Form Equivalent Circuits. 11. Special Products, Factoring, and Equations. Mentally Multiplying Two Binomials. Product of the Sum and Difference of Two Numbers. Square of a Binomial. Factoring the Difference of Two Squares. Factoring a Perfect Trinomial Square. Factoring By Grouping. Combining Several Types of Factoring. Literal Equations. 21. Applications of Logarithmic and Exponential Equations to Electronic Concepts. The Decibel. System Calculations. RC and RL Transient Behavior. Preferred Number Series. 22. Angles and Triangles. Points, Lines, and Angles. Special Angles. Triangles. Right Triangles and the Pythagorean Theorem. Similar Triangles; Trigonometric Functions. Using the Trigonometric Functions to Solve Right Triangles. Inverse Trigonometric Functions. Solving Right Triangles When Two Sides Are Known. 23. Circular Functions. Angles of Any Magnitude. Circular Functions. Graphs of the Circular Functions. Inverse Circular Functions. The Law of Sines and the Law of Cosines. Polar Coordinates. Converting between Rectangular and Polar Coordinates. PAPERBACK Fair 0130476005 Student Edition. No apparent missing pages. Heavy wear, wrinkling, creasing, Curling or tears on the cover and spine May be missing front or back cover. May have used stic...show morekers or residue. Good binding with NO apparent loose or torn pages. Heavy writing, highlighting and marker. ...show less $58.40104142.1530476005-5-0 $186.55 +$3.99 s/h New indoo Avenel, NJ BRAND NEW $186.70 +$3.99 s/h New PaperbackshopUS Secaucus, NJ New Book. Shipped from US within 4 to 14 business days. Established seller since 2000 6-30-03 other 6
Buy Used Textbook Buy New Textbook eTextbook Instant Online Access 180 day digital rental $56.49 More New and Used from Private Sellers Starting at $132Susanna Epp's DISCRETE MATHEMATICS: AN INTRODUCTION TO MATHEMATICAL REASONING provides a clear introduction to discrete mathematics and mathematical reasoning in a compact form that focuses on core topics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students develop the ability to think abstractly as they study each topic. In doing so, the book provides students with a strong foundation both for computer science and for other upper-level mathematics courses. Table of Contents Speaking Mathematically Variables The Language of Sets The Language of Relations and Functions The Logic of Compound Statements Logical Form and Logical Equivalence Conditional Statements Valid and Invalid Arguments The Logic of Quantified Statements Predicates and Quantified Statements I Predicates and Quantified Statements II Statements with Multiple Quantifiers Arguments with Quantified Statements Elementary Number Theory and Methods of Proof Direct Proof and Counterexample I: Introduction Direct Proof and Counterexample II: Rational Numbers Direct Proof and Counterexample III: Divisibility Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem
Mathematics for Elementary Teachers: A Conceptual Approach 9780073519579 ISBN: 007351957X Publisher: McGraw-Hill Summary: Would you like to rent Mathematics for Elementary Teachers: A Conceptual Approach online from Valore Books now? If you would like to take advantage of discounted prices on pre-owned copies of this book published by McGraw-Hill, look at our selection now. Written by Albert B Bennett, Laurie J Burton and Leonard T Nelson, you can find the cheapest copies of this text book by using our site now. Buy Mathematics for Elem...entary Teachers: A Conceptual Approach online from us today and find out why so many people rent and buy books for college from us. Try our website now for the cheapest deals. Bennett, Albert B. is the author of Mathematics for Elementary Teachers: A Conceptual Approach, published under ISBN 9780073519579 and 007351957X. Five hundred ninety four Mathematics for Elementary Teachers: A Conceptual Approach textbooks are available for sale on ValoreBooks.com, two hundred seventy one used from the cheapest price of $86.33, or buy new starting at $113 New Condition. SKU:9780071310024-1-0-15 Orders ship the same or next busin... [more].[less]
A guide to concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. more... Word problems are the most difficult part of any math course ?- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem. more... Solving Word Problems for Life, Grades 6-8 offers students who struggle with math a daily opportunity to improve their skills. The book offers 180 math word problems. The first 30 focus on 6th-grade math standards, the second 30 on 7th-grade standards, and the last 30 on 8th-grade standards. There is also a section of more difficult, extra-credit problems... more... As a result of the editors' collaborative teaching at Harvard in the late 1960s, they produced a ground-breaking work -- The Art Of Problem Posing -- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme... more... The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem... more... Updated and expanded, this second edition satisfies the same philosophical objective as the first -- to show the importance of problem posing. Although interest in mathematical problem solving increased during the past decade, problem posing remained relatively ignored. The Art of Problem Posing draws attention to this equally important act and is... more... Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source... more... "Advances in Discrete Tomography and its Applications" is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge... more...
Praise for the First Edition ". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a... more... Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes given for the linear algebra course at the Department... more... A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for... more... This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical... more... This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange... more... Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially... more... Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological... more...
Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography. This major textbook, a product of many years' teaching, will appeal to all teachers of combinatorics who appreciate the breadth and depth of the subject. The authors exploit the fact that combinatorics requires comparatively little technical background to provide not only a standard introduction but also a view of some contemporary problems. All of the 36 chapters are in bite-size portions; they cover a given topic in reasonable depth and are supplemented by exercises, some with solutions, and references. To avoid an ad hoc appearance, the authors have concentrated on the central themes of designs, graphs and codes. Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to anbsp;fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result. This unique approach to combinatorics is centered around challenging examples, fully-worked solutions, and hundreds of problems---many from Olympiads and other competitions, and many original to the authors. Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons. "A=B" is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks, and we intend to maintain the latest versions of the programs that carry out these algorithms on this page. So be sure to consult this page from time to time, and help yourself to the latest versions of the programs. Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate level textbook will allow students and researchers easy entry into this fascinating field. Here, for the first time, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results. ? Comprehensive graduate level textbook for a highly active current area of research ? The authors bring together for the first time the many different tools and ideas that are used in the modern theory of additive combinatorics ? The text is supplemented with a large number of exercises
Introduction to Real Analysis: An Educational Approach - 09 edition Summary: Providing a lucid and accessible introduction to the field, Introduction to Real Analysis engages readers by beginning with an AP calculus focus, and then quickly moving to the more theoretical aspects of mathematical analysis topics. Exercises and examples throughout the book range in difficulty and are both proof oriented and computational skill-building problems. This thoroughly classroom-tested book is designed to be particularly accessible and clear for future teachers of second...show moreary mathematics as well as current teachers working towards a degree in mathematics education. ...show less 2009 Hardcover Very good Ships out next day, click expedited for faster shipping. $90.04 +$3.99 s/h New PaperbackshopUS Secaucus, NJ New Book. Shipped from US within 4 to 14 business days. Established seller since 2000 $94.52 +$3.99 s/h New EuroBooks Horcott Rd, Fairford, New Book. Shipped from UK within 4 to 14 business days. Established seller since 2000. $98.12 +$3.99 s/h New Hoxton Books Southend on Sea, Somerset, New Jersey, U.S.A. 2009 Hard Back NEW Statistics BRAND NEW/UNREAD BOOK

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