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Undergraduate Texts in Mathematics

If you have not had pre-calc for two years or more, retake pre-calc! A second perspective always seems to help Get a study aid-a book of the type: "calculus for absolute morons" Never miss class Do not split the sequence. That is, do not take calc I at one school and calc II at another. Probably your second teacher will use a different approach from your first, when you have difficulty changing horses midstream, your second teacher will blame it on your first teacher having done an inferior job.

Back to Top Calculus Pedagogy. Most people come out of the calculus sequence with superficial knowledge of the subject. However, the students who survive with a superficial knowledge have always been the norm. Merely by surviving, they have shown they are the good students. The really good students will acquire a deeper knowledge of calculus with time and continued study. Those that don't are not using calculus and it is not clear why they needed to take it in the first place. Calculus, like basic algebra, is partly a course in technique.

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That is another reason to do all of your homework. There is technique and there is substance, and these things reinforce one another. People like to go from simple models and examples to abstraction later. This is the normal way to learn.

There is nothing wrong to learning the syntax of the area before the theory. Too much motivation can be as bad as too little. As you learn concepts, let them digest; play with them and study them some more before moving on to the next concept. When you get into a new area, there is something to be said for starting with the most elementary works.

For example, even if you have a Ph. You are likely to find that you will penetrate the deeper works more ably than if you had started off with deeper works. Back to Top. A basic principle is this: most serious students of mathematics start to achieve depth in any given area the second time they study it. If it has been three or four years since you had the calculus sequence, go back and study your old text; you might be surprised by how different and easier it seems and how interesting.

Often if one comes back to a discipline after a six-month layoff from that discipline, not from math it seems so different and much easier than it was before. Things that went over your head the first time now seem obvious. A similar trick that is not for everyone and that I do not necessarily recommend has worked for me. When studying a new area it sometimes works to read two books simultaneously.

That is: read a chapter of one and then of the other. Pace the books so that you read the same material at roughly the same time. The two different viewpoints will reinforce each other in a manner that makes the effort worthwhile. Serious students ask questions. Half or more of all questions are stupid. Good students are willing to ask stupid questions. Generally, willingness to ask stupid questions is a sign of intelligence. When his son decided to major in engineering, Dr.

Gullberg sat down and wrote a book containing all the elementary mathematics he felt every beginning engineer should know or at least have at his disposal. He then produced the book in camera-ready English. The result is almost a masterpiece. It is the most readable reference around.

Every freshman and sophomore in the mathematical sciences should have this book. It covers most calculus and everything up to calculus, including basic algebra, and solutions of cubic and quartic polynomials. It covers some linear algebra, quite a bit of geometry, trigonometry, and some complex analysis and differential equations, and more.

A great book: Gullberg, Jan. Mathematics From the Birth of Numbers. The following book is as friendly as any, and is well written. In many ways it is a companion to Gullberg in that it starts primarily where Gullberg leaves off.

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There is some overlap, primarily basic calculus, but I for one don't think that is a bad thing. It covers much of the mathematics an engineer might see in the last year as an undergraduate. Not only are there the usual topics but topics one usually doesn't see in such a book, such as group theory. Riley, Hobson, M. Mathematics Methods for Physics and Engineering.

It is aimed at the senior level and above. Most books on algebra are pretty much alike. For self study you can almost always find decent algebra books for sale at large bookstores closing out inventory for various schools. Algebra at this level is a basic tool, and it is critical to do many problems until doing them becomes automatic. It is also critical to move on to calculus with out much delay.

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  • For the student who has already reached calculus I suggest Gullberg as a reference. With the preceding in mind I prefer books in the workbook format. An excellent textbook series is the series by Bittinger published by Aison-Wesley. Trig like pre-calculus algebra and calculus itself tends to be remarkably similar from one text to another.

    A good example of the genre is: Keedy, Mervin L.

    MATH 2153: Calculus III

    Trigonometry: Triangles and Functions. There is a recent book about trig for the serious student. This is a much needed book and has my highest recommendation: Maor, Eli. Trigonometric Delights. Princeton University. Selected Papers on Precalculus. Stillwell, John. Numbers and Geometry. First, see Principle of Learning Calculus. Kline, Morris. There are a great many competent texts in this area. The best is Strang, Gilbert. Linear Algebra and Its Applications. It undoubtedly the most influential book in its area since Halmos's Finite Dimensional Vector Spaces. This is a more appropriate text for the classroom, especially at the sophomore level: Strang, Gilbert.

    Introduction to Linear Algebra. A more recent book along similar lines is: Curtis, Morton L. Abstract Linear Algebra.

    Mathematics | MIT OpenCourseWare | Free Online Course Materials

    Linear Algebra Done Right. An advanced applied text is: Lax, Peter D. Linear Algebra. A book emphasizing that is: Banchoff, Thomas, and John Wermer. Linear Algebra Through Geometry. It is certainly an interesting text after the first course. Linear Algebra and Its Applications , 2 nd ed.

    ISBN 10: 0387909850

    He does a nice job of introducing a surprising number of the key ideas in the first chapter. I think somehow that this has a great pedagogical payoff. Although it is very similar to many other texts, I like this particular text a great deal. Personally though I prefer the introductory text by Strang If choosing a text for a sophomore level course, I myself would choose the book by Lay or the one by Strang Wellesley-Cambridge Press.

    Calculus 1 Introduction, Basic Review, Limits, Continuity, Derivatives, Integration, IB, AP, & AB

    The following book has merit and might work well as an adjunct book in the basic linear algebra course. It is the book for the student just learning mathematics who wants to get into computer graphics.

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    Farin, Gerald and Dianne Hansford. Basic Matrix Algebra with Algorithms and Applications. Chapman and Hall. Also strong on applications. An excellent choice for a second book: Robert, Alain M.