Math 2131 (Honors in Linear and Abstract Algebra I, Fall 2025)

Teaching Site >

Basic Class Information

References

In the internet age, basic knowledge is as accessible as the air we breathe. Therefore, I do not confine myself to any particular textbook. For your reference, I have included the following three sources:

0. Linear Algebra, from Wikipedia

1. Linear Algebra, by Prof. Min Yan

2. Honors in Linear and Abstract Algebra I, by Prof. Ivan Ip

COURSE CONTENTS

• Week 1: Groups, Rings, Fields, and Vector Spaces
• Week 2: Linear Maps, Injective Linear Maps, Surjective Linear Maps, Linear Equivalences, Trivialisations, Matrix Representations
• Week 3: Subspaces, Quotient Spaces, Free Vector Spaces, Kernels, Images, Cokernels, Coimages, Sums and Direct Sums, the Canonical Forms of Linear Maps
• Week 4: Universal Properties, Exact Sequences, Finite Products, Finite Coproducts, Biproducts
• Week 5: Spans, Linearly Independent Sets, Bases, Dimension, Nullities, Ranks, Co-ranks
• Week 6: Dual Spaces and Dual Maps. Doubles. Canonical Identifications
• Week 7: Midterm Exam
• Week 8: Tensor Products, Tensors and Tensor Algebras
• Week 8: Determinant Lines and Determinants
• Week 9: Endomorphisms: its Canonical Forms
• Week 10: Euclidean Vector Spaces
• Week 11: Hermitian Vector Spaces
• Week 12: Symplectic Spaces
• Week 13: Some Further Topics

GRADING POLICY

Grades will be computed as follows:

• 20%: homework assignments
• 30%: midterm examination
• 50%: final examination

HOMEWORKS

They will be assigned weekly and announced on Canvas

EXAMS

They will be announced on Canvas