Linear Algebra

Course Description and Grading Breakdown
Math 1b is a one term course on linear algebra over the real and complex numbers. Vector spaces are defined axiomatically and proofs are supplied for most results. Topics include: vector spaces and inner product spaces; subspaces, dimension, and bases; linear transformations; systems of linear equations; matrices; determinants; eigenvalues and eigenvectors; the characteristic polynomial; symmetric, hermitian and unitary matrices; and transformations. Grading will be based roughly on 40% homework, 40% final, and 20% biweekly quizzes.

Course Meeting Time and Location
Monday, Wednesday and Friday
10:00 - 10:55 am
310 Linde

Thursday Recitations
 Section Time Location TA
5 10 am B111 DWN 
6 1 pm B127 GCL 
7 2 pm 119 DWN 

Course Instructor Contact Information and Office Hours
281 Linde Hall
Office Hours - Wednesday 12:30 - 1:30 pm

TA Contact Information and Office Hours
Andrei Frimu (Head TA)

Course Notes and Textbook
The main textbook for the course will be Tom Apostol's  Calculus, Vol. II, 2nd edition, and the material we will cover corresponds fairly closely to Chapters 1-5 in it.  However, it is not strictly necessary to buy this book for the course.  There exist many free online texts covering most of the material, such as Linear Algebra Done Wrong which would be fine as reference material.

These are some brief and rough notes of the material covered in the lectures. The file includes notes from 8 weeks of classes. I don't recommend them for learning the material, but just as a guide to what has been done.  In particular, most proofs will probably be omitted.   

If you are interested in serving as a course ombudsperson, please let Meagan know.
 HouseName Email (at
 AveryLin Lin Lee llee3
 Blacker  Madeline Gardner
Adrian Lopez
Paromita Mitchell
Limbert Palomino
 DabneyNoah Ortiz ndortiz
 Lloyd    Sabrina Rui srui
 RickettsHelena Guanwgguan
 RuddockCharlotte Park cipark

Course Policies

Students may work together on homework problems as long as each student writes up their own homework in their own words and understands the solution.

At most one late homework set will be accepted, and only at your TA's discretion, if arrangements have been made in advance with your TA, and if the work is less than a week late.  Other than in exceptional circumstances, homework will not be accepted more than a week after the deadline.

Many of the problems which will be assigned this year in Math 1b, also were assigned in previous years in Math 1b.

Do not consult the solution sets from previous years in working this years problems.


Go to the recitations! Some weeks, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA, and try to use them to fill in all the holes in your understanding of the subject.

 Date PostedAssignment Due Date 
 1/4/19 HW1 1/14/19 4 pm
 1/14/19 HW2 1/22/19 4 pm
Quiz 1
 1/24/19 4 pm

Midterm and Final Exam

Collaboration Table
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handouts/posted notesYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:


* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

Andrei Frimu,
Jan 16, 2019, 2:33 PM
Caltech Math,
Jan 4, 2019, 11:26 AM
Caltech Math,
Jan 14, 2019, 2:40 PM
Caltech Math,
Jan 14, 2019, 9:03 AM