Mathematical Thinking

This textbook invites readers to explore mathematical thinking by finding the beauty in the subject. With an accessible tone and stimulating puzzles, the author will convince curious non-mathematicians to continue their studies in the area. It has an expansive scope, covering everything from probability and graph theory to infinities and Newton's method. Many examples of proofs appear as well, offering readers the opportunity to explore these topics with the amount of rigor that suits them. Programming exercises in Python are also included to show how math behaves in action.

Mathematical Thinking is an ideal textbook for transition courses aimed at undergraduates moving from lower level to more advanced topics, as well as for math recruitment and invitational courses at the freshman or sophomore level. It may also be of interest in computer science departments and can be used as a supplemental text for courses in discrete mathematics and graph theory.

Explores mathematical thinking and encourages everyone to find the beauty in the subject Uses an accessible tone and stimulating puzzles to convince readers to continue their studies of mathematics Covers a wide range of topics in a compact form, including examples of proofs and programming exercises

Autorentext

Howard Karloff is a former professor of computer science at Georgia Tech and the University of Chicago. He is also the author of the 1991 Modern Birkhauser Classic "Linear Programming."

Inhalt

Primes.- The Euclidean Algorithm.- Modular Arithmetic.- Irrationals.- i.- Infinities and Diagonalization.- Binary Search.- Newton's Method.- Graph Theory.- Probability.- Fractals.- Solutions to Puzzles.- Acknowledgements.- Bibliography.- Index.