Elements of Mathematics
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Abstract algebra
Addition
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Algebra
Algebraic number
Arithmetic
Author_John Stillwell
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Axiom
Binomial coefficient
Bolzano-Weierstrass theorem
Calculation
Category1=Non-Fiction
Category=PBC
Coefficient
Combinatorics
Commutative property
Complex number
Computable number
Computation
Constructible number
Continuous function
Continuum hypothesis
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Dirichlet's approximation theorem
Divisibility rule
Elementary function
Elementary mathematics
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Equation
Euclidean geometry
Exponentiation
Extended Euclidean algorithm
Factorization
Fundamental theorem
Fundamental theorem of algebra
Gaussian integer
Geometry
Godel's incompleteness theorems
Halting problem
Integer
Integer factorization
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Logic
Mathematical induction
Mathematician
Mathematics
Method of exhaustion
Natural number
Non-Euclidean geometry
Number theory
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Pigeonhole principle
Polynomial
Predicate logic
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Prime factor
Prime number
Probability
Projective line
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Pythagorean theorem
Rational number
Real number
Rectangle
Reverse mathematics
Robinson arithmetic
Scientific notation
Set theory
Significant figures
softlaunch
Special case
Subset
Successor function
Summation
Theorem
Time complexity
Turing machine
Variable (mathematics)
Vector space
Zermelo-Fraenkel set theory
Product details
- ISBN 9780691171685
- Weight: 794g
- Dimensions: 152 x 235mm
- Publication Date: 31 May 2016
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity.
Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.
John Stillwell is professor of mathematics at the University of San Francisco. His many books include Mathematics and Its History and Roads to Infinity.
