Math 20850, Fall `15


Topics, reading and homework assignments are given below. Beyond a week or two out the schedule is very tentative. Hence I will update this page often. It is your responsibility to check it frequently to see what's going on in class. In particular, you will find all new homework assignments here, and soon after you turn in an assignment, I will post solutions for you to look at.







Vectors in Rn


See also Jones Chap 1

A note about lines

Homework 1


The Putnam exam is the nation's premier college math competition. All Notre Dame students are welcome to compete, and if you haven't previously done so, you can sign up for Prof Galvin's 1 credit preparatory problem-solving class. More details here.


Linear systems and matrices


A list of important definitions and results (so far) in this class

Homework 2


A group of upperclass honors math majors will be offering help for all freshman/sophomore honors math classes every Sun-Thurs 7-9 PM in the Math Bunker (partitioned off area in the math library). Take advantage of it!

Prof Connolly is organizing a topology reading group for freshman and (especially) sophomore honors math majors. Follow the link for more details.


Linear transformations and matrix algebra


Homework 3


Please point out any mistakes you catch in my homeworks, solutions, etc. To make it worth your while, I will award hwk points for corrections.

I am changing my regular office hours from Tues 5-6:30 to Wed 5-6:30.


Inverting matrices

Subspaces, bases, and dimension

4.2 (see also this note )

1.3, 4.3

Homework 4


Note that I've struck the 4.2 probs from hwk 3 and will reassign them on hwk 4.


Bases and dimension. The four fundamental subspaces associated to a matrix

4.3, 4.4

Homework 5



Visualizing non-linear function


Review for exam 1

Here are a couple of mathematica notebooks that illustrate how to graph and draw level sets of scalar-value functions and how to plot parametrized curves.


Limits and continuity

2.3 and my own notes

Homework 6


If you're interested in taking the Putnam exam, please email Prof. Galvin ( by Wed October 7 so he can sign you up.

1st exam Thursday 10/8

There will be a math for everyone talk: Exploring the Fourth Dimension in Geometry, Literature, and Art on Thursday 10/8 at 5 PM in Jordan 101. The speaker is an ND alum, Prof Thomas Banchoff of Brown University.


Partial and directional derivatives


3.1 (also Jones 2CD)

3.2 (also Jones 2EFJL)

Homework 7


This week only: my Wed office hours will be 5:30-7 instead of 5-6:30.

Mathematica notebook concerning directional derivatives

Math Autobiographical Lecture Series: Prof.and ND math alum Adam Boocher will speak in Hayes-Healy 229 on Wed, Oct 14 from 5-6 PM. See the Math Club website for more details

Math Club is holding an introductory seminar on Latex on Wed, Oct 14. Go and learn to make your math prettier…


More differentiation

The chain rule

My take

3.3 (also Jones 2K)

Homework 8



Derivatives of scalar-valued functions and of curves

Higher order derivatives

3.4, 3.5 (also Jones 2 AGH)

3.6 (also Jones 3A)

Homework 9


I need to move my Wed office hours forward a bit this week, so I'll be in 125 HH from 4:15-5:45 PM instead of the usual time.


Higher order derivatives (cont)

Topology of R^n and the extreme value theorem

Extreme Value Theorem


5.1 (and my take on the proof)

Review for exam 2

I will hold a meeting about summer math research/learning opportunities on Tuesday 11/10 from 5-6 PM in HH 229.

There will also be a math career night, complete with various math alums (& pizza) Wed 11/11 from 5-6 PM in HH 258.

There will be a math for everyone talk: Using Mathematics to Create Symmetry Patterns on Thursday 11/12 at 5 PM in Hayes-Healy 127. The speaker is ND alum and Prof Joe Gallian of U Minnesota @ Duluth.


Max/Min Problems—first and second derivative tests

5.2-5.3 (and my take on the proof of the second dervative test)

Homework 10


2nd exam Thurs 11/19


Something fun


Lagrange multipliers

Least squares solutions of linear systems



Homework 11


I will not pick up homework 11 for grading, but I will include related questions on the final. Toward the end of next week, I will post answers/solutions to some of the problems on this homework. Also, the extra credit problem on this homework is one of my favorites.


Other stuff

Review for the final exam

Final exam takes place Monday Dec 14 from 4:15-6:15 in 127 Hayes-Healy (our usual classroom).

Homework 10 is now graded. I will leave it in my mailbox (2nd floor Hurley) over the weekend for you to pick it up. On Sunday, I will hold an office hour from 2-3 PM in 125 Hayes-Healy.