Math 9700-202, Bridge Course (Algebra), Summer 2025

Resources

• Course schedule
• Slides on group theory (Mon. July 14 only)

Daily worksheets

• HW 1: pdf | tex Topic: The four fundamental subspaces. Due Thursday, July 3, 2025.
• HW 2: pdf | tex Topic: Projection and least squares. Due Monday, July 7, 2025.
• HW 3: pdf | tex Topic: Orthogonality. Due Tuesday, July 8, 2025.
• HW 4: pdf | tex Topic: Vector spaces and subspaces. Due Wednesday, July 9, 2025.
• HW 5: pdf | tex Topic: Spanning, linear independence, basis. Due Thursday, July 10, 2025.
• HW 6: pdf | tex Topic: Quotients. Due Tuesday, July 15, 2025.
• HW 7: pdf | tex Topic: The isomorphism theorems. Due Wednesday, July 16, 2025.
• HW 8: pdf | tex Topic: The dual of a vector space. Due Thursday, July 17, 2025.
• HW 9: pdf | tex Topic: Linear maps. Due Friday, July 18, 2025.
• HW 10: pdf | tex Topic: The transpose of a linear map. Due Monday, July 21, 2025.
• HW 11: pdf | tex Topic: The matrix of a linear map. Due Tuesday, July 22, 2025.
• HW 12: pdf | tex Topic: Multilinear forms. Due Wednesday, July 23, 2025.
• HW 13: pdf | tex Topic: Determinant and trace. Due Thursday, July 24, 2025.
• HW 14: pdf | tex Topic: Eigenvalues. Due Friday, July 25, 2025.
• HW 15: pdf | tex Topic: Eigenvectors and generalized eigenvectors. Due Monday, July 28, 2025.
• HW 16: pdf | tex Topic: Eigenspaces and Jordan canonical form. Due Tuesday, July 29, 2025.
• HW 17: pdf | tex Topic: Inner products. Due Wednesday, July 30, 2025.
• HW 18: pdf | tex Topic: Adjoints. Due Thursday, July 31, 2025.
• HW 19: pdf | tex Topic: Quadratic forms, left and right inverses. Due Friday, August 1, 2025.
• HW 20: pdf | tex Topic: Singular value decomposition, pseudo-inverses. Due Monday, August 4, 2025.