Blast Into Math!
 Price: 129.00 kr
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 Price: 129.00 kr
 Price: 129.00 kr
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About the book
Reviews
Jemil Alvarez ★★★★★
I think the book is very clear and that it strengthens those who don't understand math.
Sorin NeaguVentzel ★★★★★
Excellent one! I will use it for sure with my students who are preparing for math contests. Thanks!
Chanaka Sudheera ★★★★★
A very useful textbook!
Zohaib Nasir ★★★★★
I think by reading this anyone can increase their ability to solve math problems. :)
Raymond D. Deans ★★★★★
This is for students who are starting off in learning the subject, and a good reinforcement to those who find it to be difficult.
Description
Blast into Math! A fun rigorous introduction to pure mathematics which is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style. Definitions, theorems, and proofs are accompanied by creative analogies and illustrations to convey the meaning and intuition behind the abstract math. The key to reading and understanding this book is doing the exercises. You don't need much background for the first few chapters, but the material builds upon itself, and if you don't do the exercises, eventually you'll have trouble understanding. The book begins by introducing fundamental concepts in logic and continues on to set theory and basic topics in number theory. The sixth chapter shows how we can change our mathematical perspective by writing numbers in bases other than the usual base 10. The last chapter introduces analysis. Readers will be both challenged and encouraged. A parallel is drawn between the process of working through the book and the process of mathematics research. If you read this book and do all the exercises, you will not only learn how to prove theorems, you'll also experience what mathematics research is like: exciting, challenging, and fun!
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Content
 Preface
 To the reader
 Pure mathematics: the proof of the pudding is in the eating
 A universal language
 Theorems, propositions, and lemmas
 Logic
 Ready? Set? Prove!
 Exercises
 Examples and hints
 Sets of numbers: mathematical playgrounds
 Set theory
 Numbers
 The least upper bound property
 Proof by induction
 Exercises
 Examples and hints
 The Euclidean algorithm: a computational recipe
 Division
 Greatest common divisors
 Proof of the Euclidean Algorithm
 Greatest common divisors in disguise
 Exercises
 Examples and hints
 Prime numbers: indestructible building blocks
 Ingredients in the proof of the Fundamental Theorem of Arithmetic
 Unique prime factorization: the Fundamental Theorem of Arithmetic
 How many primes are there?
 Counting infinity
 Exercises
 Examples and hints
 Mathematical perspectives: all your base are belong to us
 Number bases: infinitely many mathematical perspectives
 Fractions in bases
 Exercises
 Examples and hints
 Analytic number theory: ants, ghosts and giants
 Sequences: mathematical ants
 Real numbers and friendly rational numbers
 Series: a tower of mathematical ants
 Decimal expansions
 The Prime Number Theorem
 Exercises
 Examples and hints
 Afterword
 Bibliography