Course: MATH 115A, Linear Algebra, Lecture 6, Fall 2014
Prerequisite: MATH 33A, Linear algebra and applications.
Course Content: Linear independence, bases, orthogonality, the Gram-Schmidt process,
linear transformations, eigenvalues and eigenvectors, and diagonalization of matrices. This course
should develop your ability to write rigorous proofs.
Last update: 11 December 2014
Lecture Meeting Time/Location: Monday, Wednesday and Friday,
1PM-150PM, MS5147
Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Mondays, 930AM-1130AM, Fridays, 1030AM-1130AM, MS
7370
TA: Geunho Gim,
ggim(@-symbol)math.ucla.edu
TA Office Hours: Thursdays, 9AM-11AM, MS 2344
Discussion Session Meeting Time/Location: Tuesday and Thursday, 1PM-150PM,
MS5147
Required Textbook: Linear Algebra, Friedberg, Insel and Spence, 4th
Ed., Custom Edition for UCLA
Other Textbooks (not required): Linear Algebra: an introductory approach, C. W. Curtis
TA Course Website: here
First Midterm: October 31, 1PM-150PM, FRANZ 2258A
Second Midterm: November 24, 1PM-150PM, PUBLIC AFFAIRS 2250
Final Exam: December 15, 8AM-11AM, BOELTER 5440
Other Resources:
115A, Tao, Fall 2002: I would highly recommend
reading these lecture notes. My own lecture notes below are meant to be a more condensed presentation of similar material. So, if you
prefer a more thorough treatment, I recommend these notes (and the book).
An
introduction to mathematical
arguments, Michael Hutchings,
An Introduction to Proofs,
How to Write Mathematical Arguments
Exam Procedures: Students must bring their UCLA ID cards to the
midterms and to the final exam. Phones must be turned off. Cheating on
an exam results in a score of zero on that exam. Exams can be
regraded at most 15 days after the date of the exam.
Exam Resources: Here
is a page containing old exams
for a similar linear algebra course. Occasionally these exams will cover
slightly different material than this class, or the material will be in a
slightly different order, but generally, the concepts
should be close if not identical.
Here are solutions to
this
second midterm. (Note this practice midterm is much longer than our
exam.)
Here are solutions to
this
practice final. (Skip question 7; also questions 5,6 and 8 are a bit
challenging.)
Homework Policy:
Tentative Schedule: (This schedule may change slightly during the course.)
Week | Monday | Tuesday | Wednesday | Thursday | Friday |
0 | Sep 29 | Oct 2: No homework due | Oct 3: 1.2, Vector spaces | ||
1 | Oct 6: 1.3, Subspaces | Oct 8: 1.4, 1.5, Linear systems, Linear independence | Oct 9: No homework due | Oct 10: 1.5, 1.6, Linear independence, bases | |
2 | Oct 13: 1.6, Dimension | Oct 15: 1.6, Lagrange interpolation | Oct 16: Homework 1 due | Oct 17: 2.1, Linear transformations | |
3 | Oct 20: 2.1, Linear transformations | Oct 22: 2.1, 2.2, Null spaces, range, coordinate bases | Oct 23: Homework 2 due | Oct 24: 2.2, Matrix representation | |
4 | Oct 27: 2.3, Matrix Multiplication | Oct 29: 2.4, Invertibility | Oct 30: Homework 3 due | Oct 31: Midterm #1 | |
5 | Nov 3: 2.4, Isomorphism | Nov 5: 2.4, 2.5, Change of coordinates | Nov 6: Homework 4 due | Nov 7: 2.5, Change of coordinates | |
6 | Nov 10: 3.1-4.3, Review of matrices | Nov 12: 4.4, Review of determinants | Nov 13: Homework 5 due | Nov 14: 5.1, Diagonal matrices | |
7 | Nov 17: 5.1, Eigenvalues and eigenvectors | Nov 19: 5.2, Diagonalization | Nov 20: Homework 6 due | Nov 21: 5.2, Characteristic polynomials | |
8 | Nov 24: Midterm #2 | Nov 26: 6.1, Inner products | Nov 27: No class | Nov 28: No class | |
9 | Dec 1: 6.1, 6.2, Norms, orthogonal bases | Dec 3: 6.2, Gram-Schmidt orthogonalization, complements | Dec 4: Homework 7 due | Dec 5: 6.3, Adjoints | |
10 | Dec 8: 6.4, Normal operators | Dec 10: 6.4, Self-adjoint operators | Dec 11: Homework 8 due | Dec 12: Catch up, review |
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