Blast Into Math!
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Summary
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.
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About the book
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
About the Author
Julie Rowlett is an American mathematician currently teaching and researching pure mathematics at the University of Goettingen and the Max Planck Institute for Mathematics in Germany. Her research focus is geometric analysis. She received her Bachelor of Science in Mathematics from the University of Washington in 2001 and PhD in Mathematics from Stanford University in 2006. Her postdoctoral research experience includes the Centre de Recherches Mathematiques in Montreal, the Mathematical Sciences Research Institute in Berkeley, and the Hausdorff Center for Mathematics in Bonn. Julie has taught courses at Stanford University for the Education Program for Gifted Youth, at the University of California Santa Barbara, and at the University of Goettingen (in German). In addition to math, she enjoys cooking, learning foreign languages, singing, and dancing.
Henry Segerman is a British/American mathematician, currently working as a research fellow at the University of Melbourne in Australia. He received his Master of Mathematics degree from the University of Oxford in 2001 and his PhD in Mathematics from Stanford University in 2007. He was a postdoctoral lecturer at the University of Texas at Austin from 2007 to 2010, and will start an assistant professorship position at Oklahoma State University in 2013. In addition to his research in 3dimensional geometry and topology he is a mathematical artist, having exhibited works in art exhibitions at the Joint Mathematics Meetings and the Bridges conferences on mathematics and the arts. He is also an associate editor for the Journal of Mathematics and the Arts. He works mainly in the medium of 3D printed sculpture, but occasionally dabbles in 2D work, including of course illustration! See www.segerman.org for many more mathematically artistic projects.
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Reviews
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.
Paul Ziegler ★★★★★
Book Boon has been publishing free books for several years now. I am completing one of their newest mathematics texts, "Blast into Math." It is an excellently written book about mathematical logic using number theory as a means of illustrating how mathematicians think and work. Excelent book, excellent website.
Hlazo Ngwenya ★★★★☆
it's a good book especially for those that find mathematics uninteresting .