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From the preface: Prerequisites. The mathematical prerequisites are minimal: no particular mathematical concepts beyond what is taught in a typical undergradua
by xyzzyz 11y ago
From the preface:
Prerequisites. The mathematical prerequisites are minimal: no particular mathematical
concepts beyond what is taught in a typical undergraduate calculus
sequence are assumed.
The computer science prerequisites are also quite minimal: it is assumed that the
reader is proficient in programming, and has had some exposure to the analysis of
algorithms, essentially at the level of an undergraduate course on algorithms and
data structures.
Even though it is mathematically quite self contained, the text does presuppose
that the reader is comfortable with mathematical formalism and also has
some experience in reading and writing mathematical proofs. Readers may have
gained such experience in computer science courses such as algorithms, automata
or complexity theory, or some type of “discrete mathematics for computer science
students” course. They also may have gained such experience in undergraduate
mathematics courses, such as abstract or linear algebra. The material in these mathematics
courses may overlap with some of the material presented here; however,
even if the reader already has had some exposure to this material, it nevertheless
may be convenient to have all of the relevant topics easily accessible in one place;
moreover, the emphasis and perspective here will no doubt be different from that
in a traditional mathematical presentation of these subjects
- anton-107 11y agoWhat would be a good textbook for Math 101, specifically to learn some advanced mathematical formalism without actually diving in applied science behind it?
- nextos 11y agoI really like Hubbard & Hubbard.
- tdsamardzhiev 11y agoCoursera's Calculus One and Calculus Two courses. I've found other branches of math to be much easier to understand if you have basic knowledge about calculus.
- tomku 11y agoKeeping with the free theme, Book Of Proof by Richard Hammack is a nice introduction to proofs and formalism. It's available free from the author as a PDF[1], and also as a physical book on Amazon[2]. An alternative if you're willing to spend a little is How to Prove It by Daniel J. Velleman, also available from Amazon[3] and probably many other retailers. Both books cover roughly the same topics. [1]: http://www.people.vcu.edu/~rhammack/BookOfProof/ http://www.people.vcu.edu/~rhammack/BookOfProof/ [2]: http://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472108 http://www.amazon.com/Book-Proof-Richard-Hammack/dp/09894721... [3]: http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995 http://www.amazon.com/How-Prove-It-Structured-Approach/dp/05...
- jordigh 11y agoThis stuff is usually rolled into courses called "abstract algebra". If a textbook is called "abstract algebra", it's usually designed for a first year undergraduate. If it's just called "algebra", it's usually aimed at a more mature audience. Herstein and Hungerford are the texts I learned from. This book seems more recent and popular: http://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472108/ http://www.amazon.com/Book-Proof-Richard-Hammack/dp/09894721... The other big stream of basic undergraduate mathematics is analysis. For that I recommend Spivak's Calculus.