Mathematics 110
Spring, 2020
MW
5:106:30PM,
155 Dwinelle Hall
Graduate student instructors
 Nic
Brody
 Kubrat
Danailov
 Ian
Andrei A Gleason Freidberg
 Christopher
Kuo
 Luhang
Lai
 Alexander
Bertoloni Meli
Catalog description
"Matrices, vector spaces, linear transformations, inner products,
determinants. Eigenvectors. QR factorization. Quadratic forms and
Rayleigh's principle. Jordan canonical form, applications. Linear
functionals"
Textbook
Linear Algebra Done Right
by Sheldon Axler.
If you are in berkeley.edu, you can download a free, legal electronic
copy of this book from the
book's
page
on Springer link.
This same page should display a link for you to buy a
high quality softcover edition for $24.99 (including shipping).
You might want to consult
the author's
twitter feed
and especially his
LADR videos.
Axler's book
was based partly on ideas from
his article
Down with Determinants!,
which is fun to read.
Class schedule
Date  Themes  Sections 
Jan. 22 
Introduction to the course

Fields, vector spaces

Subspaces


1.A, 1.B, 1.C

Jan. 27 
Subspaces

Span, linear independence

The replacement lemma


1.C, 2.A

Jan. 29   
Feb. 3   
Feb. 5   
Feb. 10   
Feb. 12   
Feb. 19   
Feb. 24 
First Midterm Exam 
Feb. 26   
Mar. 2   
Mar. 4   
Mar. 9   
Mar. 11   
Mar. 16   
Mar. 18   
Mar. 30   
Apr. 1 
Second Midterm Exam 
Apr. 6   
Apr. 8   
Apr. 13   
Apr. 15   
Apr. 20   
Apr. 22   
Apr. 27   
May. 1   
May. 4 
Review 
May. 6 
Questions 
May. 15 
Final Exam, 3:006:00PM 
Examinations
 First
midterm exam, Monday, February 24, 2020, in class;
 Last
midterm exam, Wednesday, April 1, 2020, in class;
 Final
examination, Friday, May 15, 2020, 36PM.
Please do not plan travel on the dates of these exams.
If you believe that you have a conflicting obligation because of an
intercollegiate sport or other
extracurricular activity,
please read
these
guidelines
immediately.
For each exam, you may bring in a single 2sided 8 1/2 x 11 sheet of
paper with your notes for the exam. The opportunity
to create your page of notes will likely
guide your review of the material for the exam.
For practice
I seem to have taught Math 110 six times before:
 Fall, 2002: this was a
fairly
large course in 3 LeConte;
 Fall, 2003: this was the honors section of
Math 110;
 Spring, 2005: this was a large class in
10 Evans;
 Fall, 2008: this was a class
using Linear Algebra Done Right,
but it was taught to a class of about 35 students;
 Spring, 2010: this was a large class in
10 Evans.
 Spring, 2014: a large class followed Axler's book
as beta testers for the third edition of LADR.
Each course page should have links
to problems and solutions for
the exams in the course.
Note that some midterms were 50 minutes long while others were
80 minutes long.
Grading
Course grades
will be based on a weighted average of
the exam and homework grades. In 2014,
the weights were as follows:
midterm exams 17% each, homework
20%, final exam 46%.
Incomplete
grades will be assigned only to students for whom a documented
medical, personal or family emergency precludes completion of the course.
Students receiving such grades are required to have been doing work
of passing quality up to the occurrence of the emergency.
In 2014, I checked the historical grade distribution for
Math 110 and came up with:
36% A, 34% B, 21% C, 9% D/F.
Note that many students who received an F grade had effectively
abandoned
the course after the add/drop deadline.
You can read the
handwritten
student evaluations
for the spring, 2014 version of this course.
Homework
Assignments will be due in section on Fridays:
 Due January 24
 Due January 31:

§1.A, problem 11

§1.B, problems 1, 6

§1.C, problems 1cd, 3, 5, 7, 8, 9, 10, 12, 13, 15, 23
 §2.A, problems 3, 5, 6
 Due February 7:
 §2.A, problems 8, 9, 10, 11, 14, 17
 §2.B, problems 1, 3, 5, 7, 8
 Valentine's Day:
 §2.C, problems 1, 7, 8, 9, 10, 12, 13, 14
 §3.A, problems 3, 4, 8, 9, 10, 11, 12, 14
 §3.B, problems 1, 2, 5, 6
 February 21:
 §3.B, problems 7, 15, 19, 26
 §3.C, problems 2, 3, 4
 §3.D, problems 3, 4, 5, 7, 9, 10, 16, 19
 §3.E, problems 7, 8, 9
 February 28:
 §3.E, problems 3, 10, 11, 12, 13, 14, 16
 §3.F, problems 3, 4, 6
 March 6:
 §3.F, problems 7, 9, 11, 19, 20, 21, 22, 23, 34, 35
 Chapter 4, problems 2, 3, 6, 7, 8, 10
 March 13:
§5.A, problems 1, 3, 6, 8, 12, 13, 15, 19, 23, 24
 March 20:
 §6.A, problem 11—due in class on March 16, but
not to be handed in
 §5.B, problems 1, 10, 2, 3, 4, 8, 9, 11
 §5.C, problems 1, 3, 5, 16
 April 3:
 §6.A, problems 3, 4, 5, 7, 8, 12
 §6.B, problems 2, 5, 6, 7, 8, 13
 April 10:
 §6.C, problems 3, 5, 6, 7, 8 (uses exercise 6.A.6)
 §7.A, problems 2, 3 (done in class), 4, 5, 6, 9, 10, 11, 12
 April 17:
 §7.B, problems 3, 4, 6, 8, 10, 11, 12, 13, 14
 §7.C, problems 1, 2, 4, 7, 8, 9, 11
 April 24:
 §7.D, problems 1, 2, 4, 10, 12, 13
 §8.A, problems 3, 4, 6, 8, 9, 11, 14
 May 1:
 §8.B, problems 2, 4, 5, 10, 11
 §8.C, problems 1, 2, 4, 7, 10, 11, 12, 15
 May 8 (RRR period):
 §8.D, problems 1, 3, 5, 6
 §9.A, problems 6, 9, 10, 11, 13, 15, 17
 §9.B, problems 3, 4, 5, 6
Each assignment
after the first
will be worth 10 points. Your homework grade will
be the sum of your twelve highest grades and half of your
nexttolowest grade. Accordingly, the maximum possible homework
grade will be 125; we are "dropping" 1 1/2 assignments in computing
your score.
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