This book will help students in mathematics and other quantitative subjects to fill in the gaps in their preparation for graduate school. It presents the basic points, a few key results, and an annotated reading list of the most important undergraduate topics in mathematics: linear algebra, vector calculus, geometry, real analysis, point-set topology, and more.
This book will help students in mathematics and other quantitative subjects to fill in the gaps in their preparation for graduate school. It presents the basic points, a few key results, and an annotated reading list of the most important undergraduate topics in mathematics: linear algebra, vector calculus, geometry, real analysis, point-set topology, and more.
Preface On the structure of mathematics Brief summaries of topics 1. Linear algebra 2. e and d 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. Complex analysis 10. Countability and the axiom of choice 11. Algebra 12. Lebesgue integration 13. Fourier analysis 14. Differential equations 15. Combinatorics and probability 16. Algorithms A. Equivalence relations.
Preface On the structure of mathematics Brief summaries of topics 1. Linear algebra 2. e and d 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. Complex analysis 10. Countability and the axiom of choice 11. Algebra 12. Lebesgue integration 13. Fourier analysis 14. Differential equations 15. Combinatorics and probability 16. Algorithms A. Equivalence relations.
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