This course is a proof-based continuation of Math 250, covering abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms.
Instructor: Yi-Zhi Huang
- Office hours: Monday and Wednesday 3:20-4:40 and by appoitment, Hill 332
- Email: email@example.com. Questions by email are welcome.
- Prerequisites for Section H1: CALC4, Math 250, Math 300 and permission of the department.
- Text: Linear Algebra, 5th ed., by Friedberg, Insel and Spence, Prentice Hall, 2019, ISBN 978-0134860244.
- Lectures: MW6, 5:00-6:20 pm in ARC-333, Busch campus.
- First midterm exam: Wednesday, October 9, 2019, 5:00--6:20 pm in ARC-333.
- Second midterm exam: Wednesday, November 20, 2019, 5:00--6:20 pm in ARC-333.
- Final exam: Tuesday, December 17, 2019, 12:00 noon--3:00 PM. The final exam room will be announced later, but most likely will be at the regular lecture room.
- Quizzes: Quizzes will be given at the ends of a few class sessions. The dates of these quizzes, and the topics covered, will be announced in advance.
- Homework: Homework is due on most Wednesdays. There is no HW due on the two midterm-exam Wednesdays.
- Homework policy: You are allowed, and encouraged, to discuss with other people and also to ask me for hints, either by email or in class or in office hours. But your final HW writeups must be your own, expressed in your own way and showing your own understanding. Also, nowadays it is easy to find solutions to problems in textbooks, including this book. But in order to really benefit from the HW (and in order to be able to do your best on the exams), you of course should not seek out or use existing solutions while you are working on the homework problems.
- Grading policy: First midterm exam: 100 points; Second midterm exam: 100 points; Homework and quizzes: 100 points; Final exam: 200 points (Total: 500 points).
- Class attendance: Class attendance is very important. A lot of what we do in class will involve collective participation.
The course is strongly based on Math 250. However, we will work axiomatically, starting from the abstract notions of vector space and linear transformation. Much of the homework and many of the exam and quiz problems will require you to write precise proofs, building on your proof-writing experience in Math 300. From this more abstract viewpoint, we will be developing linear algebra far beyond Math 250, with new insight and new applications.
We will cover the topics indicated in the syllabus below, but the dates that we cover some of the topics might be adjusted during the semester, depending on the material covered and discussed.
Review notes on Math 250, prepared by Eugene Speer.
Additional review problems for Exam 1
Answers and proofs of additional review problems for Exam 1
Tentative Course Syllabus
|1||9/4||Chapter 1||Abstract vector spaces, subspaces|
|2||9/9, 9/11||Chapter 1||Subspaces, span of subsets, linear independence, bases and dimension|
|3||9/16, 9/18||Chapter 1||Bases and dimension, Linear transformations|
|4||9/23, 9/25||Chapter 2||Matrix representation, composition|
|5||9/30, 10/2||Chapter 2||Invertibility, change of basis, dual spaces|
|6||10/7, 10/9||Ch. 1-2||Review and Exam 1|
|7||10/14, 10/16||Chapter 3||Rank and systems of linear equations|
|8||10/21, 10/23||Chapter 4||Determinants and their properties|
|9||10/28, 10/30||Chapter 5||Eigenvalues, eigenvectors, diagonalizability|
|10||11/4, 11/6||Ch. 5 & 7||Invariant subspaces, Jordan canonical form|
|11||11/11, 11/13||Chapter 7||Jordan canonical form|
|12||11/18, 11/20||Ch. 3-5, 7||Review and Exam 2|
|13||11/25||Chapter 6||Inner product spaces|
|14||12/2, 12/4||Chapter 6||Inner product spaces, normal and self-adjoint operators|
|15||12/9, 12/11||Chapter 6||Unitary and orthogonal operators, review|
|12/17||Ch. 1-7||Final Exam (12:00 noon--3:00 pm; room to be announced, likely in the regular classroom ARC-333)|
Homework Assignments and Additional Comments
|Due on:||Homework Problems|
|9/11||1.2: #9, 12, 17; 1.3: #8(a), (e), 18, 19, 23.|
|9/18||1.4: #4(a), 5(g), 12,14; 1.5: #2(e), 9,15.|
|9/25||1.6: #3(a),(b), 15, 21, 26; 2.1: 3, 9(a)-(e), 15, 28. (Hand in problems in 2.1 on 9/30.)|
|10/2||2.2: #2(a), (g), 4, 8, 10; 2.3: #3(a),(b), 4(d) , 12.|
|10/16||2.4: #2(f), 9, 15; 2.5: #3(d), 5, 8; 2.6: #2(a), (d), (e), 3, 4.|
|10/23||3.1: #6,12; 3.2: #5(d), (h),17; 3.3: #8,10; 3.4: #8,14|