Download PDF Theoremus: A student's guide to math proofs, by Dr. L P Cruz
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Theoremus: A student's guide to math proofs, by Dr. L P Cruz
Download PDF Theoremus: A student's guide to math proofs, by Dr. L P Cruz
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This concise textbook will teach mathematics students the art of proving theorems. Using a simple approach, it will provide them the mechanics to solve challenging proof exercises. Students are first taught to be sensitive to fallacious claims so they could form valid assertions. The book shows the proper use of logic and its deduction rules. It is an effective tool for improving students’ skills in formulating sound mathematical arguments. What is more is that the student can get all of these in one sitting.
- Sales Rank: #2488933 in Books
- Published on: 2015-01-02
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .20" w x 5.50" l, .31 pounds
- Binding: Paperback
- 82 pages
About the Author
L.P. Cruz is a mathematician and logician who has worked in the IT profession for over 20 years. He has taught a wide range of mathematics-oriented subjects related to computer science. He is passionate in helping students overcome their struggles with university level mathematics. When not teaching, he works as a consultant specialising in functional programming and data analysis. In his spare time he conducts research on the application of logic to machine learning problems.
Most helpful customer reviews
0 of 0 people found the following review helpful.
A Handy, Readable Reference with Appropriate Depth
By Pdecordoba
Disclaimer: I was given a free copy of this book by the author.
“Theoremus” succeeds in its purpose: to be complete enough to serve not only math majors, but students of any subject that requires them to do proofs, while also being of a handy “booklet” size that can be carried from class to class and from study group to study group. Cruz’s writing style is friendly and humorous without being superficial, and he doesn’t neglect to mention that – the humorous aspects of mathematical work notwithstanding – writing proofs of non-trivial assertions requires dedication, practice, and hard work.
The author begins the book by making a convincing case for why proofs are needed, and therefore for why we need to be able to understand them and do them. Most importantly, of course, we wish to avoid falling into erroneous thinking. But we cannot avoid erroneous thinking if we don’t understand what does and does not constitute a proof. As the the author notes in the Preface, “If there is no appreciation for how theorems are proved, mathematics [including the algorithms that students are required to learn] becomes a magical art fogged by mystery. The students won’t even know why these algorithms work.”
Cruz devotes an appropriate portion of the book to examples of proofs and to exercises in which the students must write their own. He prepares readers for that work by discussing the nature of mathematical assertions, and of the “well established and agreed rules of reasoning” that we must follow in order to construct a compelling proof. Coverage of those subjects is of sufficient depth while remaining true to Cruz’s intention of producing a convenient, booklet-sized volume. Particularly helpful are his examples of fallacious “proofs”, and his list of the types of assertions that we are allowed to use to link our premise to the conclusion that we wish to prove: those assertions may follow from a definition; from an axiom; from previously proven assertions (e.g., theorems); or from an application of the rules of logic or deduction. No other type is allowed.
I intend to make that list into a poster, and hang it on the wall in my classroom.
The book ends with an observation that’s also made in Thinking Mathematically (2nd Edition): that the closely-reasoned, finely-written proofs presented to students in textbooks are often the result of a long, messy, and chaotic – but ultimately successful – effort to prove notions that occurred to mathematicians through intuition, imagination, and subjective sense of “beauty”. Encouraging words, indeed, for students who may be facing with dread the fact that a course that they MUST pass requires them to do proofs!
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