Blast Into Math!

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( 61 )
215 pages
Idioma:
 English
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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Sobre el autor

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...

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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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  • Preface
  1. To the reader
  2. Pure mathematics: the proof of the pudding is in the eating
    1. A universal language
    2. Theorems, propositions, and lemmas
    3. Logic
    4. Ready? Set? Prove!
    5. Exercises
    6. Examples and hints
  3. Sets of numbers: mathematical playgrounds
    1. Set theory
    2. Numbers
    3. The least upper bound property
    4. Proof by induction
    5. Exercises
    6. Examples and hints
  4. The Euclidean algorithm: a computational recipe
    1. Division
    2. Greatest common divisors
    3. Proof of the Euclidean Algorithm
    4. Greatest common divisors in disguise
    5. Exercises
    6. Examples and hints
  5. Prime numbers: indestructible building blocks
    1. Ingredients in the proof of the Fundamental Theorem of Arithmetic
    2. Unique prime factorization: the Fundamental Theorem of Arithmetic
    3. How many primes are there?
    4. Counting infinity
    5. Exercises
    6. Examples and hints
  6. Mathematical perspectives: all your base are belong to us
    1. Number bases: infinitely many mathematical perspectives
    2. Fractions in bases
    3. Exercises
    4. Examples and hints
  7. Analytic number theory: ants, ghosts and giants
    1. Sequences: mathematical ants
    2. Real numbers and friendly rational numbers
    3. Series: a tower of mathematical ants
    4. Decimal expansions
    5. The Prime Number Theorem
    6. Exercises
    7. Examples and hints
  8. Afterword
  9. Bibliography
awsome maths learning experience
3 de enero de 2017, 15:28
I think the book is very clear and that it strengthens those who don't understand math.
10 de febrero de 2015, 1:43
Excellent one! I will use it for sure with my students who are preparing for math contests. Thanks!
20 de agosto de 2014, 12:37
A very useful textbook!
4 de junio de 2014, 7:04
I think by reading this anyone can increase their ability to solve math problems. :-)
28 de marzo de 2014, 17:02
This is for students who are starting off in learning the subject, and a good reinforcement to those who find it to be difficult.
6 de mayo de 2013, 14:01
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.
24 de abril de 2013, 15:31
it's a good book especially for those that find mathematics uninteresting .
11 de febrero de 2013, 5:32
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