Transition to Advanced Mathematics A Survey Course

Name: Transition to Advanced Mathematics A Survey Course
Price: 30.22 USD
Availability: InStock
ISBN: 9780195310764

ISBN-10: 0195310764

ISBN-13: 9780195310764

Edition: 2009

Authors: William Johnston, Alex McAllister

List price: $145.00

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A Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing theintriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective of A…

Book details

List price: $145.00
Copyright year: 2009
Publisher: Oxford University Press, Incorporated
Publication date: 7/27/2009
Binding: Hardcover
Pages: 768
Size: 10.00" wide x 7.28" long x 1.60" tall
Weight: 3.520
Language: English




Mathematical Logic



The Formal Language of Sentential Logic



Truth and Sentential Logic



An Algebra for Sentential Logic



Application: Designing Computer Circuits



Natural Deductive Reasoning



The Formal Language of Predicate Logic



Fundamentals of Mathematical Proofs


Notes



Abstract Algebra



The Algebra of Sets



The Division Algorithm and Modular Addition



Modular Multiplication and Equivalence Relations



An Introduction to Groups



Dihedral Groups



Application: Check Digit Schemes


Notes



Number Theory



Prime Numbers



Application: Introduction to Coding Theory and Cryptography



From the Pythagorean Theorem to Fermat's Last Theorem



Irrational Numbers and Fields



Polynomials and Transcendental Numbers



Mathematical Induction


Notes



Real Analysis



Analytic Geometry



Functions and Inverse Functions



Limits and Continuity



The Derivative



Understanding Infinity



The Riemann Integral



The Fundamental Theorem of Calculus



Application: Differential Equations


Notes



Probability and Statistics



Combinatorics



Pascal's Triangle and the Binomial Theorem



Basic Probability Theory



Application: Statistical Inference and Hypothesis Testing



Least Squares Regression


Notes



Graph Theory



An Introduction to Graph Theory



The Explorer and the Traveling Salesman



Shortest Paths and Spanning Trees



Application: Weighted Graphs


Notes



Complex Analysis



Complex Numbers and Complex Functions



Analytic Functions and the Cauchy-Riemann Equations



Power Series Representations of Analytic Functions



Harmonic Functions



Application: Streamlines and Equipotentials


Notes


Answers to Questions


Answers to Odd-Numbered Exercises


Online Resources


References


Index