PH 610: Mathematical Methods for Scientists
Fall 2022 (D. Belitz)
Chapter 1: Algebraic Structures
$1: Sets, and mappings
1.1 Sets
1.2 Mappings
1.3 Ordered sets
1.4 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: Fields
3.1 Bilinear mappings
3.2 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
$5: Tensor fields
5.1 Tensor fields
5.2 Gradient, curl, divergence
5.3 Tensor products and tensor traces
5.4 Minkowski tensors
Chapter 2: Topics in Analysis