A First Book in Algebra

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Practical Genetic Algorithms. Coding and Information Theory.

Pre-Algebra - Basic Introduction!

Note that coding theory is different from cryptography. That is a different type of coding. There is one fairly informal non-technical beautifully written book on information theory by a great engineer and it is cheap! There are two books that are quite good by Steven Roman. I suggest that one read the first. If you want to continue deeper into the subject, by all means obtain the second: Roman, Steven.

Introduction to Coding and Information Theory. Error-Coding Codes and Finite Fields. Introduction to the Theory of Error-Correcting Codes. It covers information theory and more. The author is one of the best writers on applied mathematics.

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Fairly large book. Luenberger, David G. Information Science. The second edition will include recommendations on books on Digital Filters and Signal Analysis. The books listed here are all calculus based except for the book by Bennett.. An absolutely superb book for the layman, and of interest to the professional accomplishes what many other books have merely attempted. Bennett, Deborah J.

Mystery Math: A First Book of Algebra by David A. Adler

See also Tanur. An interesting book, quite philosophical, on randomness is the one by Taleb. One of the best books written for the undergraduate to learn probability is the book by Gordon. Despite the restriction to discrete probability this book is a superb general introduction for the math undergraduate and is very well organized.

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Mystery Math: A First Book of Algebra

Gordon, Hugh. Discrete Mathematics. As a rule I think that the best books to learn probability from are those on modeling. For example, perhaps the best writer on probability is Sheldon Ross.

Introduction to Probability Models , 6 th ed. Karlin, Samuel. An Introduction to Stochastic Modeling , rev. It is indeed a wonderful book: Hamming, R. The Art of Probability for Scientists and Engineers. Elementary Probability, 2 nd ed.

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Problems and Snapshots from the World of Probability. The first volume is inspiring. The larger second volume is even more technical than the first, for example there is a chapter review of measure theory. Feller, William. Introduction to Probability Theory.

Vol 2, 2 nd ed. The following is an inexpensive little reference. It requires only a basic knowledge of probability, say through Bayes' Theorem. The great thing about it is that the problems are actually interesting. I have found this to be a good source for classroom examples.

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Mosteller, Frederick. Fifty Challenging Problems in Probability with Solutions. Duelling Idiots and Other Probability Puzzlers. Fuzzy Stuff logic and set theory. Some books in this area are better than others.

By in large though, it is a lot of bull about ad hoc, not particularly robust, algorithms. Claims of anything new and profound are general pompous bullstuff. Fuzzy methods are trivial if you have knowledge of probability and logic. In my view the aspiring applied mathematician can not do better than to study probability.

A book of practical statistics as opposed to mathematical or theoretical statistics is the one by Snedecor and Cochran. It is rigorous but does not use calculus. It uses real life biological data for examples but is fascinating. It is a wonderfully well written and clear book. A real masterpiece. Anyone who actually does statistics should have this book.

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But remember, though it does not require calculus it does require mathematical maturity. My feeling is that if you want to use this book but do not know calculus you should go back and take calculus. Snedecor, George W. Statistical Methods , 8 th ed.


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Iowa State. A great book. The best books about statistics for the layman are very likely: Tanur, Judith M. Statistics: A Guide to the Unknown , 3 rd ed. This is a great book. See also Bennett. Salsburg, David.