All the Math You Missed (2/e)
豆瓣
But Need to Know for Graduate School
Thomas A. Garrity
简介
Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.
contents
On the structure of mathematics
Brief summaries of topics
1. Linear Algebra
2. and real analysis
3. Calculus for vector-valued functions
4. Point set topology
5. Classical Stokes' theorems
6. Differential forms and Stokes' theorem
7. Curvature for curves and surfaces
8. Geometry
9. Countability and the Axiom of Choice
10. Elementary number theory
11. Algebra
12. Algebraic number theory
13. Complex analysis
14. Analytic number theory
15. Lebesgue integration
16. Fourier analysis
17. Differential equations
18. Combinatorics and probability theory
19. Algorithms
20. Category theory
Appendix A. Equivalence relations
References
Index.
