Math 350H: Linear Algebra (Honors)
Instructor: Joseph Palmer
Email: j.palmer at rutgers.edu
Schedule: 1:40-3:00pm Mondays and Wednesdays in HLL-009
Textbook: Linear Algebra 4th ed. by Friedberg, Insel, and Spence (ISBN: 0-13-008451-4; ISBN13: 9780130084514)
Office Hours: Wednesdays 10am-noon in my office
Sakai: You can check your grades in this course with
sakai.
This page is for a past section of this course (spring 2017) and is no longer active.
About this course:
This course is a proof-based approach to linear algebra.
The topics we discuss will be very similar to those covered in Math 250, but
these topics will be presented in a completely different manner.
We will cover nearly
the entire textbook, which encompasses the following five general topics:
- Abstract vector spaces (Ch 1)
- Linear Transformations (Ch 2, 3)
- The determinant (Ch 4)
- Eigenvectors and Canonical forms (Ch 5, 7)
- Inner product spaces (Ch 6)
Keep in mind that this is the
honors section
of this course, so it will be noticably more difficult than the other sections.
We will cover the topics to a greater depth and at a greater speed.
Grade Breakdown:
20% Homework and quiz grades (the lowest grade in this category is dropped)
20% Midterm 1
20% Midterm 2
40% Final Exam
Solutions and notes:
Chapter 1 Quiz Solutions
Midterm 1 Solutions
Determinant notes
Midterm 2 Solutions
Homework Assignments:
Instructions to turn in homework:
Put your homework assignments in the box labeled "Math 350 homework" on the door
to my office (Hill 340).
Homework 1 - due Wednesday, Jan 25th:
Section 1.2: 1, 7, 8, 13, 17, 21
Notes: Remember to be very formal in these proofs.
Mention which properties (V1)-(V8) you are using and be sure to be
careful about "for all" and "there exists".
(there are no proofs or arguments needed in problem 1)
Homework 2 - due Friday, Feb 3rd at noon:
Section 1.3: 6, 8ab, 11, 23, 27
Section 1.4: 1c (and PROVE your answer for 1c), 5g, 10, 12, 15
Section 1.5: 7 (and prove answer)
Suggested problems (not required)
Section 1.3: 5, 13, 17, 18, 30, 31
Section 1.4: 4, 8, 13, 14
Section 1.5: 3, 5, 18
Homework 3 - due Friday, Feb 10th at noon:
Section 1.6: 4, 11, 22, 26 (include proof, hint: find a basis), 34a
Suggested problems (not required)
Section 1.6: 1, 15, 19, 28, 29, 35
Homework 4 - due Friday, Feb 17th at noon:
Section 2.1: 10, 12, 15, 16, 18
Section 2.2: 3, 5d
Section 2.3: 9, 11
Suggested problems (not required)
Section 2.1: 2, 6, 8, 9, 11, 14, 17, 19, 21
Section 2.2: 5, 8, 9
Section 2.3: 1, 3, 12
Suggested problems (to study for sections 2.4, 2.5 on Midterm 1, not required):
Section 2.4: 2, 3, 4, 6, 9, 13, 14, 15, 16
Section 2.5: 2, 5, 10
Homework 5 - due Friday, March 3rd at noon:
Section 2.4: 6, 15
Section 2.5: 10
Section 3.1: 6
Section 3.2: 4
Suggested problems (not required)
Section 3.2: 2, 3, 17
Homework 6 - due Friday, March 10th at noon:
Section 3.3: 4a, 5, 8a, 10
Section 3.4: 2ab, 5
Suggested problems (not required)
Section 3.3: 2, 3, 4, 7, 8
Section 3.4: 2
Homework 7 - due Friday, March 24th at noon:
Section 4.2: 2, 14, 21, 26, 30
Section 4.3: 10, 11, 12, 14, 15, 16
Suggested problems (not required)
Section 4.2: 24
Section 4.3: 13, 20
Homework 8 - due Friday, March 31st at noon:
Section 4.3: 21
Section 5.1: 3a, 4e, 7a, 12, 20, 21, 24
Section 5.2: 3ab, 8, 9a
Suggested problems (not required)
Section 5.1: 2, 3, 4, 8, 9
Section 5.2: 2, 3, 7, 11
Homework 9 - due Friday, April 7th at noon:
Section 5.4: 2ab, 3, 6d, 8, 11, 12, 19
Suggested problems (not required)
Section 5.4: 2, 5, 6, 7, 13, 16, 17
Homework 10 - due Friday, April 28th at noon:
Section 7.1: 4, 10
Section 6.1: 6, 10, 16b, 17, 23ab
Section 6.2: 2c, 4, 7, 15, 16
Suggested problems (not required)
Section 7.1: 2ab (just find Jordan form - not the basis), 5
Section 6.1: 5, 8, 9, 15
Section 6.2: 2, 3, 5, 8, 11 (also 6, 13c, 23)
Suggested problems for 6.3 - 6.6 (not required to be turned in)
Section 6.3: 2, 4, 7, 8, 9, 11
Section 6.4: 2, 3, 11
Section 6.6: 5, 7bdfg
FINAL EXAM IS ON TUESDAY MAY 9th
The final will cover everything we have talked about in class so far, with extra emphasis placed on Chapter 6.
It is good to be familiar with the sorts of problems on Midterm 1 and Midterm 2
and the assigned and suggested homework problems for all the sections
(especially Chapter 6).
Tentative Schedule:
This will be updated throughout the semester to stay as accuate as possible.
| | Date | Sections | Topics |
|---|
| 1: | 1/18 | 1.1, 1.2 | Vector spaces |
| 2: | 1/23 | 1.2, 1.3 | More vector spaces, Subspaces |
| 3: | 1/25 | 1.3 | Subspaces HW1 (Sec 1.2) |
| 4: | 1/30 | 1.4, 1.5 | Linear independence |
| 5: | 2/1 | 1.5, 1.6 | Bases and dimension HW2 (Sec 1.3, 1.4, 1.5) |
| 6: | 2/6 | 1.6 | Bases and dimension |
| 7: | 2/8 | 2.1 | Linear transformations HW3 (1.6) |
| 8: | 2/13 | 2.2 | Matrices |
| 9: | 2/15 | 2.3, 2.4 | Composition and isomorphisms HW4 (2.1, 2.2, 2.3) |
| 10: | 2/20 | 2.5, (2.6) | Change of Coordinates, (and dual spaces) |
| | 2/22 | | Midterm 1: Chapters 1 and 2 |
| 11: | 2/27 | 3.1, 3.2 | Elementary matrices, rank, and matrix inverses |
| 12: | 3/1 | 3.3, 3.4 | Systems of linear equations HW5 (2.4, 2.5, 3.1, 3.2) |
| 13: | 3/6 | Chap 4 | The determinant |
| 14: | 3/8 | Chap 4 | Uniqueness of determinant HW6 (3.3, 3.4) |
| 15: | 3/20 | Chap 4 | Properties of determinant |
| 16: | 3/22 | 5.1 | Eigenvalues and eigenvectors HW7 (4.2, 4.3) |
| 17: | 3/27 | 5.1 | Eigenvalues and eigenvectors |
| 18: | 3/29 | 5.2 | Diagonalizability HW8 (5.1, 5.2) |
| 19: | 4/3 | 5.4 | Invariant subspaces and Cayley-Hamilton Theorem |
| 20: | 4/5 | 7.1 | Jordan form HW9 (5.4) |
| 21: | 4/10 | 7.1 | Jordan form |
| | 4/12 | | Midterm 2: Chapters 3, 4, 5, 7 |
| | 4/17 | | Catch up (finish 7.1), talk about Midterm |
| 22: | 4/19 | 6.1 | Inner product spaces |
| 23: | 4/24 | 6.2 | Gram-Schmidt |
| 24: | 4/26 | 6.3, 6.4 | Adjoints HW10 (7.1, 6.1-6.3) |
| 25: | 5/1 | 6.4, 6.6 | Normal/Self-Adjoint operators and the Spectral Theorem |
| - | 5/9 | | FINAL EXAM (12-3pm in HLL-009) |