PH 410/510: Mathematical Methods for Scientists
Spring 2013 (D. Belitz)
Chapter 1: Elements of Algebra
$1: Sets, and mappings
1.1 Sets
1.2 Mappings
1.3 Compositions of mappings
1.4 Ordered sets
1.5 The natural numbers, and the principle of mathematical induction
$2: Groups
2.1 The definition of a group
2.2 Rules of operation
2.3 Permutations
2.4 Subgroups
2.5 Isomorphisms and authomorphisms
$3: Rings and fields
3.1 Bilinear mappings
3.2 Rings and fields
3.3 The field of complex numbers
$4: Vector spaces and tensor spaces
4.1 Vector spaces
4.2 Basis sets
4.3 Tensor spaces
4.4 Dual spaces
4.5 Metric spaces
4.6 Banach spaces
4.7 Hilbert spaces
4.8 Generalized metrics, Minkowski space
Chapter 2: Topics in Analysis