- Michael Daub Office hours Fri 1-3, 737 Evans
- Yael Degany Office hours Tues 11:35-2:00, 1060 Evans
- Thomas DeIonno Office hours Wed 12-2, 1093 Evans
- James McIvor Office hours Thu 11:30-1:30, Fri 11-12, 1070 Evans

**Lectures:** TuTh 2-3:30pm, 10 Evans Hall

**Discussion Sections:** Wednesdays,
see Schedule

**Course Control Number:** 54242

Incomplete grades are rarely given, and only in documented cases of illness or serious personal or family emergency. A grade of Incomplete for missing work can only be given if you having passing grades on your other work.

Each assignment will consist of a number of *Exercises*,
relatively straightforward problems which will **not** be graded,
and a smaller number (from 1 to 3) of *Problems*,
which **will** be graded. You do not have to hand in the
Exercises, but you should nevertheless do them carefully, both to
check your understanding of the material and as preparation for the
Problems and for exams. Generally speaking, exam questions will be
similar to the Exercises or some of the less difficult Problems.

You are free to discuss ideas on how to solve the Problems with other students. However, you must write your solutions independently. It is not permissible to copy solutions worked out in a group, or from students who took the class before, or found on the web.

No late or make-up homework will be accepted. When calculating grades, we will drop two scores and use only your best scores remaining.

- Midterm 1, Thursday Feb. 16, in two rooms:
- Last names A–M in 105 Stanley (opposite Evans across the Mining Circle)
- Last names N–Z in 10 Evans (the regular lecture room)

- Midterm 2, Thursday Mar. 22, same rooms as Midterm 1

Final Exam Monday, May 7, 11:30-2:30pm (Exam Group 2), Room
1 Pimentel
Hall.

At midterm exams you may bring one (ordinary size) sheet of notes, written on both sides. Two sheets are allowed for the final exam. No other books, calculators, computers or other aids may be used. Space to write answers will be provided on the exam paper, but you should bring your own scratch paper.

No make-up exams will be given. If you miss one midterm, your score on the following exam will count for that midterm. However, you cannot "miss" a midterm retroactively after turning in your exam. If you miss the final or both midterms, see the discussion of Incomplete grades under Grading Policy, above.

- Vector spaces.
- Subspaces. Intersections and sums; direct sums.
- Span, linear independence and bases. Dimension of a finite-dimensional vector space.
- Linear maps.
- Nullspace, range and rank of a linear map.
- Matrix of a linear map.
- Invertible linear maps.
- Eigenvalues and eigenvectors.
- Inner product spaces.
- Orthonormal bases and the Gram-Schmidt procedure.
- Orthogonal projections; applications.
- Adjoints.
- Self-adjoint and normal operators; spectral theorem.
- Positive operators and isometries; polar and singular-value decompositions.
- Operators on complex vector spaces.
- Characteristic polynomials and minimal polynomial.
- Jordan form.

- Reading for Lectures 1-3: Axler, Chapters 1 and 2. Homework Assignment 1, due Friday, Jan. 27. Solutions
- Reading for Lectures 4-6: Axler, Chapters 2 and 3. Homework Assignment 2, due Friday, Feb. 3. Solutions
- Reading for Lectures 7-8: Axler, Chapter 3. Homework Assignment 3, due Friday, Feb. 10. Solutions
- Midterm 1 is Thursday, Feb 16, in two rooms (see above). The
subject matter is the contents of Homeworks 1 to 3, that is, Axler
chapters 1-3 plus the material from the lectures
on
*F*and on span, independence and bases for infinite-dimensional spaces which was covered in the homework exercises. You can find the first midterm (with solutions) from my Fall 2009 Math 110 class along with links to some older exams here: Haiman Math 110 Fall 09._{2} - Midterm 1 Solutions
- Reading for Lectures 9-11: Axler, Chapter 3, continued. Homework Assignment 4, due Friday, Feb. 24. Solutions (updated Mar. 5).
- Reading for Lectures 12-13: Axler, Chapter 10 (Change of Basis only), Chapter 4 (review of polynomial algebra), Chapter 5. Homework Assignment 5, due Friday, Mar. 2. Solutions (updated Mar. 5).
- Reading for Lectures 14-15: Axler, Chapter 5. Homework Assignment 6, due Friday, Mar. 9. Solutions (this link erroneously gave HW 5 before, now fixed).
- Reading for Lectures 15-16: Axler, Chapter
6. Homework Assignment 7, due
Friday, Mar. 16 (updated Mar. 14: the assigned problem was too hard,
so I
**changed it**). Solutions - Midterm 2 is Thursday, Mar. 22 in the same two rooms as before: last names A–M in 105 Stanley, last names N–Z in 10 Evans. The subject matter is the contents of Homeworks 4-7.
- Midterm 2 Solutions
- Reading for Lectures 18-20: Axler, Chapter 6: Orthogonal
Projections and Minimization; Linear Functionals and
Adjoints. Homework Assignment 8, due
Friday, Apr. 6.
**Hint for Problem 1**: the hardest part is figuring out how to use the hypothesis*||Pv||≤||v||*. To get an idea about this, try working out an example of a projection*P*in*R*which is not orthogonal, and see for which vectors the hypothesis fails. Solutions^{2} - Announcement: Prof. Haiman's office hours on Wed., Apr. 4 will be 1-2:30pm (back to normal next week).
- Reading for Lectures 21-22: Axler, Chapter 7: Self-Adjoint and Normal Operators, Isometries. Don't miss Lecture 21! It will cover some topics not in the book. Homework Assignment 9, due Friday, Apr. 13. Solutions
- Reading for Lectures 23-24: Rest of Axler, Chapter 7, but omitting Normal Operators on Real Inner Product Spaces. Homework Assignment 10, due Friday, Apr. 20. Solutions
- Reading for Lectures 25-26: Axler, Chapter 7: Singular Value Decomposition. Axler, Chapter 8, omitting Square Roots and The Minimal Polynomial. Homework Assignment 11, due Friday, Apr. 27. Solutions
- Professor Haiman's RRR week office hours are W-Th 11-12.
- Final Exam Monday, May 7 (details under Exams, above). You can bring two note sheets to the final. Please also bring (and use!) scratch paper. The final will cover material from the whole course, with extra emphasis on subject matter from Homeworks 8-11.
- Final Exam Solutions