# Linear Algebra

## Syllabus

Date Sections(s) Topics covered
Mathematical Induction. An introduction to prooves. How many prime numbers are there?
1.2 Fields and vector spaces
1.2, 1.3 Vector spaces and subspaces
1.3, 1.4 Subspaces and linear combinations
Linear Combinations
1.5, 1.6 Linear dependence and indendence, bases
1.6 Bases and dimension
1.6 Bases and dimension
2.1 Linear Transformations
2.1 Nullspace and Range
Exam 1 In class portion of first exam
Take Home Exam given out
2.1 Rank and Nullity
2.1, 2.2 Matrix representation of a linear map
Take Home Exam Due
2.2, 2.3 Matrix representation of linear transformations
2.3, 2.4 Matrix repensentations, compositions
2.4 Invertibility and Isomorphism
2.4 Invertibility and Isomorphism
3.1, 3.2 Elementary matrices and rank of matrices
3.1 - 3.4 Systems of equations, Elementary matrices
3.1 - 3.4 Systems of equations, Elementary matrices
Exam 2 In class portion of second exam
Take Home Exam given out
2.5 Change of Basis
4.2 - 4.4 An overview of determinants
5.1 Eigenvalues and eigenvectors
5.2 Diagonalizability
5.2 Diagonalizability
5.2 Diagonalizability
Chapter 6 Inner Product Spaces
Chapter 6 Inner Product Spaces