- Series: Student Mathematical Library (Book 53)
- Paperback: 182 pages
- Publisher: American Mathematical Society (June 18, 2010)
- Language: English
- ISBN-10: 0821849778
- ISBN-13: 978-0821849774
- Product Dimensions: 5.5 x 0.5 x 8.5 inches
- Shipping Weight: 8.5 ounces (View shipping rates and policies)
- Average Customer Review: 8 customer reviews
- Amazon Best Sellers Rank: #1,130,216 in Books (See Top 100 in Books)
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Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra (Student Mathematical Library)
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Finding examples of "linear algebra in action" that are both accessible and convincing is difficult. Thirty-three Miniatures is an attempt to present some usable examples. . . . For me, the biggest impact of the book came from noticing the tools that are used. Many linear algebra textbooks, including the one I use, delay discussion of inner products and transpose matrices till later in the course, which sometimes means they don't get discussed at all. Seeing how often the transpose matrix shows up in Matousek's miniatures made me realize space must be made for it. Similarly, the theorem relating the rank of the product of two matrices to the ranks of the factors plays a big role here. Most linear algebra instructors would benefit from this kind of insight. . . . Thirty-three Miniatures would be an excellent book for an informal seminar offered to students after their first linear algebra course. It may also be the germ of many interesting undergraduate talks. And it's fun as well. --Fernando Q. Gouvêa, MAA Reviews
[This book] is an excellent collection of clever applications of linear algebra to various areas of (primarily) discrete/combinatiorial mathematics. ... The style of exposition is very lively, with fairly standard usage of terminologies and notations. ... Highly recommended. --Choice
About the Author
Ji í Matou ek: Charles University, Prague, Czech Republic
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The only other thing I wish is that Professor Matousek writes a sequel and yes, I have a different opinion than his; I am most willing to see his four A4 sheets rule bend (Prof Matousek has rarely included items which exceed four A4 sheets, he does not call them a miniature).
This is a kind of entertaining math book about algebraic combinatorics for a physicist or mathematician from a different field.
Starting from miniature 22, chapters become a bit complex for me, so I had no time to go through them yet.
In any case, recommend to my colleagues, theoretical physicists, if they are curious about this topic.
The book has 33 "chapters" of 1-4 pages each (most are two pages) and in each a proof is suggested first (so you can try to work it out) and then reveled. Basic theorems from undergraduate linear algebra come in handy, but very little advanced knowledge is needed. A pen a paper will help on some of the proofs but most can be done just by thinking.
What makes it all especially exciting is that the proofs are useful! many suggest fun ideas for applications.
Since it's presented in little bite-sized chunks you can put it down at any moment.
I think any undergrad who has taken linear algebra, grad students and mathematics instructors and professors would enjoy this book. I couldn't help but share one or two of these little gems with my students!