Daily Assignments
Week 0: August 24 – 25
August 24: Fields
- Please read the syllabus.
- Claim your account on WeBWorK through Blackboard.
- Read Section 1.1-2 of the online notes
- Begin working on Problem Set 1
Week 1: August 28 – September 1
August 29: Vectors and Vector Spaces
- Finish section 1.2, and read sections 2.1-2 of the online notes.
- Finish the tutorial assignment on WeBWorK
August 31: Vector Spaces and Subspaces
- Problem Set 1 due
- Read section 2.3 and start section 2.4 of the online notes.
- Finish 1.2 Complex Numbers on WeBWorK
Week 2: September 4 – 8
September 5: Subspaces and Matrices
- Finish section 2.4 of the online notes.
September 7: Linear Combinations and Linear Equations
- Problem Set 2 due
- Section 2.5 of the online notes.
Week 3: September 11 – 15
September 12: Spanning Sets
- Slides from class
- Read section 2.6 of the online notes
September 14: Linear Independence and bases
- WeBWorK set on solving linear equations
- Problem sets now due on Tuesdays
- Read section 2.7 of the online notes
Week 4: September 18 – 22
September 19
- Problem Set 3 due
- Finish section 2.7 of the online notes
September 21
- Read the solutions to problem set 3
- Start section 3.1 of the notes.
Week 5: September 25 – 29
September 26
- Problem Set 4 due
- Section 3.2 of the notes
September 28
- Read solutions to homework 4
- Section 3.3 of the notes
Week 6: October 2 – 6
Week 7: October 9 – 11
October 10: Midterm!
But no Problem Set 6 due any more
October 12: fall break, no class
Week 8: October 16 – 20
Week 9: October 23 – 27
October 24:
- Problem Set 7 due Tuesday, October 24
Week 10: October 30 – November 3
October 31:
- Problem Set 8 due Tuesday, October 24
Week 11: November 6 – 10
- Problem Set 9 due Tuesday, November 7
Week 12: November 13 – 17
Thanksgiving Break: November 20-24
Get some rest!
Week 13: November 27 – December 1
Week 14: December 4 – 8
Finals Week
Course notes
Problem Sets
- Problem Set 1 due Thursday, August 31
- Problem Set 2 due Thursday, September 7
- Problem Set 3 due Thursday, September 14
- Problem Set 4 due Tuesday, September 26
- Problem Set 5 due Tuesday, October 3
- Note you also have two WeBWorK sets.
- Solutions
- Problem Set 6 due Tuesday, October 17
- Problem Set 7 due Tuesday, October 24
- Problem Set 8 due Tuesday, October 31
- Problem Set 9 due Tuesday, November 7
- Problem Set 10 due Tuesday, November 14
- Problem Set 11 due Tuesday, November 28
- Problem Set 12 due Tuesday, December 2
- Problem Set 13 do before final
Tests
- Midterm on Tuesday, October 10
- Practice Midterm
- Final Exam date Tuesday, December 19 10:20 AM – 12:20 PM
- As scheduled by the registrar
- Per the syllabus, you will not be excused from the final if you schedule travel during finals week; if you must buy your plane ticket before the registrar announces final exam, please make sure it departs after December 19.
- Practice Final
Calculators will not be allowed on tests.
Textbook
The official textbook for Math 2185 is Linear Algebra, 5th edition by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence. Access to this book will not strictly be required but it will be a useful reference throughout the course. As of the time I’m writing this, there appear to be cheap paperback copies on Amazon.
There are other excellent references you may find helpful. Linear Algebra Done Right, and the new fourth edition is freely available. A similar, freely available book is Linear Algebra Done Wrong by Sergei Treil.
For a more geometric and computational perspective, you may find the online source Interactive Linear Algebra very helpful. It has many manipulable graphics that can help you develop geometric and algebraic intuition.
Course Goals
This is our rigorous, proof-based linear algebra course, intended for math majors and students in other majors (e.g., computer science, data science, economics, or statistics) who want a deeper conceptual understanding than is offered in Math 2184. Math majors, prospective math majors, and students who intend to take Math 3125 should be encouraged to take this course. The theory of vector spaces is developed from the axioms and linear algebra is studied over arbitrary fields (with an emphasis on \(\mathbb{R}\) and \(\mathbb{C}\) in examples). This allows students to work with important vector spaces in addition to \(\mathbb{R}^n\). Linear transformations also take a more central role than matrices, with matrices serving as a computational tool in the finite-dimensional case.
Complete proofs of most results are presented, and students are expected to develop a mastery of proving results in linear algebra. As Math 2971 is a corequisite (or prerequisite), it is appropriate to include brief discussions of proof techniques when relevant. In addition to conceptual understanding, the course also emphasizes both the computational and geometric aspects of linear algebra.
This course is part of a two-course sequence, along with Math 3125 (Linear Algebra II), which further develops the theory of linear algebra, but also covers applications to statistics, computer science, and physics. The comprehensive introduction to linear algebra given in Math 2185 prepares students to fully understand the mathematics behind these applications.