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12. Algebraic Equations and Convex Bodies

13. N

14. Hints, Answers, and Solutions

15. Schubert Polynomials

16. The Littlewood–Richardson Rule

17. Arrays and Schur Polynomials

18. Properties of Pipe Dreams

19. Combinatorial Presentation of Schubert Polynomials

20. Arrays and Condensation Operations

21. The Symmetric Group

22. The Ring of Symmetric Functions

23. The Number of Young Tableaux

24. Combinatorial Formula for Schur Polynomials

25. Symmetric Polynomials

26. Schur Polynomials

27. Problem Set 2

28. Introduction

29. Infinite Product Factorisation of Theta Functions

30. Complex Elliptic Integrals

31. Complex Jacobian Elliptic Functions

32. Riemann Surfaces of Algebraic Functions

33. Elliptic Curves

34. Theta Functions

35. Characterisation by Addition Formulae

36. The General Theory of Elliptic Functions

37. The Abel–Jacobi Theorem

38. Addition Theorems

39. The Weierstrass ℘-Function

40. Applications of Jacobi’s Elliptic Functions

41. Mapping the Upper Half Plane to a Rectangle

42. Jacobi’s Elliptic Functions on

43. Applications of Elliptic Integrals

44. The Arc Length of Curves

45. Classification of Elliptic Integrals

46. Problem Set 3

47. Problem Set 1

48. Comparison Theorems, Curvature and Topology, and Laplacian

49. Lie Groups

50. Riemannian Manifolds

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