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Relational Algebra Tuple Relational Calculus Domain Relational Calculus

1 Mathematical Preliminaries and Error Analysis 2 Solutions of Equations in One Variable 3 Interpolation and Polynomial Approximation 4 Numerical Differentiation and Integration 5 Initial-Value Problems for Ordinary Differential Equations 6 Direct Methods for Solving Linear Systems 7 IterativeTechniques in Matrix Algebra 8 ApproximationTheory 9 Approximating Eigenvalues 10 Numerical Solutions of Nonlinear Systems of Equations 11 Boundary-Value Problems for Ordinary Differential Equations 12 Numerical Solutions to Partial Differential Equations

1 Fundamentals 2 Collections 3 Counting and Relations 4 More Proof 5 Functions 6 Probability 7 Number Theory 8 Algebra 9 Graphs 10 Partially Ordered Sets

Number Theory 1. Six proofs of the infinity of primes …… 3. Binomial coefficients are (almost) never powers 4. Representing numbers as sums of two squares …… 8. Some irrational numbers 9. Three times π2/6 Geometry 10. Hilbert’s third problem: decomposing polyhedra63 11. Lines in the plane and decompositions of graphs …… 15. The Borromean rings don’t exist …… 17. Every large point set has an obtuse angle 18. Borsuk’s conjecture Analysis …… 21. The fundamental theorem of algebra …… 25. Cotangent and the Herglotz trick 26. Buffon’s needle problem Combinatorics 27. Pigeon-hole and double counting …… 32. Cayley’s formula for the number of trees 33. Identities versus bijections …… 36. The Dinitz problem247 37. Permanents and the power of entropy253 …… 41. Communicating without errors 42. The chromatic number of Kneser graphs …… 44. Probability makes counting (sometimes) easy

《高等代数研讨 Discussions in Advanced Algebra》课程教学资源：教学大纲

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