Fall-2022. Math H110 (class # 21775): Honors Linear Algebra

Instructor: Alexander Givental
Lectures: TuTh 9:30--11 in 70 Evans
Office hours: Wednesday, 2--4, in 701 Evans
Textbook: Linear Algebra wich is my own E-book
Syllabus: the whole book perhaps less two sections ("Tensors" and "The Minkowski--Hasse theorem"), and with the Epilogue on "Quivers" used as review material during the RRR week.
Quizzes: weekly, in class (in the first 5 min), on Tu
Homework: weekly, due on Th, most likely via Gradescope

Grading policies:

Here is an ingenious (in my view) scheme of my own invention which I tried successfully in several courses and intend to use it this time. The starting point is: 40% weekly quizzes + 30% weekly hw + 30% final. However: each individual quiz or hw score which is below than or equal to (percentage-wise) your score on the final will be dropped - together with its weight! E.g.: if all your hw scores are above and all quizzes below your score on the final, then your total score is composed of 50% hw and 50% final. Thus, there are many reasons why you want to take quizzes and do hw (as well as many other exercises, not assigned as hw); yet a particular quiz/hw score can only improve your overall performance, but can never hurt your ultimate result compared to the final exam.

Besides, I don't have a preconceived distribution of As,Bs,..., and will be happy to give everyone an A should everyone learn the material well (for which I hope very much, especislly that the subject is interesting and simple). What exactly it means to learn well will become clear after some quizzes.

Thus, the general idea is that you don't compete with each other, but rather strive to learn the material the best you can. Respectively, collaboration and/or use of outside sources are not prohibited (tests excluded). Yet, each instance of this should be explicitly acknowledged in your homework. Failure to acknowledge one's use of somebody else's ideas is commonly known as academic plagiarism. So, let's practice the right ethics.


QZ1, Tu, Aug. 30. This will be a one-question/5-min quiz on Complex numbers at the start of Lecture 2. To prepare, read Section 2 on your own (and don't assume that you know complex numbers :-)
HW1, Due Th, Sep. 1: Read Sections 1 and 3. Solve all exercises from Section 1, write down your solutions to the exercises 6,9,22,25,27, and submit them for grading.

QZ2, Tu, Sep. 6: Classification of quadratic curves (Section 3).
HW2, due Th, Sep. 8: Read Section 4 of Ch 1 and Section 1 of Ch 2. Solve exercises 60, 62, 69, 83, 98.

QZ3, Tu, Sep. 13: Axioms of vector spaces.
HW3, due Th, Sep. 15: Read Section 2 of Chapter 2. Solve exercises 147, 150, 154, 157, 159.

QZ4, Tu, Sep. 20: Matrices of linear maps.
HW4, due Th, Sep. 22: Read Section 3 of Chapter 2. Solve exercises 173, 176, 178, 189, 195.

QZ5, Tu, Sep. 27: Permutations.
HW5, due Th, Sep. 29: Read Section 3 (Three Cool Formulas) of Chapter 2 and Section 1 of Chapter 3. Solve exercises 197, 222, 223, 225, 233.

QZ6, on Tu, Oct. 4: Rank.
HW6, due Th, Oct. 6: Read Section 2 of Chapter 3. Solve exercises 273, 276, 279, 281, 286.

QZ7, on Tu, Oct. 11: Bruhat cells.
HW7, due Th, Oct. 13: Read Section 3 of Chapter 3. Solve exercises 288, 289, 290(e), 291(a), 237.

QZ8, on Tu, Oct. 18: Conics.
HW8, due Th, Oct. 20: Read Section 3 of Chapter 3 and subsection "Hermitian Spaces" in Section 1 of Chapter 4. Solve: 306, 307, 308, 311, 314.

QZ9, on Tu, Oct. 25: Gram-Schmidt orthogonalization.
HW9, due Th, Oct. 27: Read Section 1 of Chapter 4 and start reading Section 2. Solve: 325, 328 (using Sylverter's rule), 329, 356, 364.

QZ10, on Tu, Nov. 1: Euclidean spaces.
HW10, due Th, Nov. 3: Read Section 2 of Chapter 3 to the end. Solve: 370, 374, 383, 399, 401(b).

QZ11, on Tu, Nov. 8: Applications of the Real Spectral Theorem.
HW11, due Th, Nov. 10: Read Section 2 and the first two subsections of Section 3. Solve: 403, 405, 408, 410, 415.

QZ12, on Tu, Nov. 15: Root spaces.
HW12, due Th, Nov. 17: Read Section 3. Solve: 420, 423, 427(d), 432, 434.

No quizzes on Tu, Nov. 22 and Nov. 29, nor hw due Th Nov. 24.

HW13, due TUESDAY, Nov. 29: Read Section 4. Solve: 438, 440, 441, 444, 445(h).

Answers to HW

Sample finals to regular Math 110, without solutions
Sample final to honors Math 110, with solutions