Math 272: Linear Algebra With Applications
||tleise at amherst dot edu
Feel free to drop in whenever my door is open, or make an appointment
Regular hours: MWF 11am-noon and 2-4pm; Tues 9am-noon
Custom version of Linear Algebra with Applications by Gareth Williams
(available at Amherst Books and on reserve in Merrill Science Library)
- Become proficient in matrix manipulations as well as the linear algebra theory
- Learn to write proofs involving essential concepts in linear algebra
- Learn some applications of linear algebra and how to apply its ideas
- Learn the “language” of linear algebra and how to communicate your mathematical ideas correctly
- Linear algebra provides an elegant framework on which more advanced mathematics is built, so this course can be a great stepping stone to prepare you for further mathematics courses, as well as preparing you to use the ideas of linear algebra in other disciplines like economics or physics.
- Solving systems of linear equations.
- Vector spaces, subspace, span, linear independence, basis, and dimension.
- Linear transformations and their matrix representations in different bases.
- Kernel or null space, range, rank, inverse, determinant, trace of a matrix.
- Characteristic polynomial, eigenvalues and eigenvectors, diagonalization.
- Basic matrix manipulations including row operations and multiplication.
- Orthogonality and inner products, with application to least squares.
- Project: linear algebra of Google and PageRank.
Attendance: You are
to be in class and to be there on time. Cooperative learning is more
and more fun than struggling through material on your own.
If you do
miss a lecture, it is your responsibility to obtain the material that
missed and to get your assignments handed in to me.
have a question during lecture, please raise your hand and ask it right
Chances are that other students are wondering the same thing. If a
arises later, feel free to visit my office and we'll work through
problems until you are comfortable with the mathematics.
Always feel free to ask me to slow down
Grading: Your course grade will be based on
three in-class exams (50% total), homework/worksheets/labs/projects (25%), and the final exam
If you are unsure what agrees or
does not agree with the precepts of intellectual responsibility in this
course, feel free to talk to me about it.
- Exams. Your work must be entirely your own, so
please follow the guidelines of the honor code. Unless I explicitly
allow other aids, you are only allowed whatever implements you need to
read and write (no notes or calculators or electronic devices). Please turn off your
cell phone in kindness to your fellow test-takers.
- Labs. Sending or receiving a copy of a Mathematica file that contains student work violates the honor code and will be treated as plagiarism. You may talk with others about strategies for solving a problem in Mathematica, but please do not share files.
- Homework. You may study with other students
following these guidelines:
- If you worked with or received help
from any source other than me, you should put a note on the front of
your homework saying, "I worked with <names>."
Make sure your name stands out as the author of your
- Working together does not mean that
one of you does the first half of the homework set and the other does
the second. Everyone should work on every problem.
- Each student must hand in his or her
own problem set. You may not hand in a single packet as the work of
- Do not copy someone else's
solution—you will not learn anything and it is plagiarism.
You may discuss problems with others, but then you must be
able to work out the solution on your own again and write it down
- All problem sets are due at THE
START OF CLASS.
Late homework will receive half credit for homework handed
in after start of class but within 2 class days (e.g., homework due
Monday will get half-credit if handed in after the start of class on
Monday through Wednesday start of class, and will not accepted after
- If you are unable to attend class due
to illness or an emergency, let me know as soon as you can and we will
work out an appropriate schedule for assignments.
- Your name should be written on all
sheets handed in.
- Problem solutions must be written out
in the order they were assigned.
- Multiple pages must be stapled.
Repeat: PLEASE STAPLE!
- Homework should be neat.
No dog ears. No messy edges
from notebook paper.
- Where appropriate, please box or
highlight final answers. In general, try
to make your answers readable and easy to find. Always
keep the grader happy!
- As mentioned elsewhere, no copying!
- Organize important definitions, theorems, and methods into a sheet and make sure you have them memorized. Start preparing and memorizing the items on this sheet well in advance of the exam so you have them in long-term memory (and not just short-term memory, which is less reliable under exam pressure).
- After reviewing the material and working some review problems, take the practice exam under exam-like conditions, without notes or the text and in the same room, if possible, as the exam itself. Memory recall can be strongest when you are physically in the same location as where you learned it or used it, and taking exams has been found to increase performance on the next similar exam. So use these facts to your advantage!
- Be aware of psychological influences like stereotype threat. If you think about reasons you won't do well or even about negative stereotypes that may apply to you, your exam performance can be detrimentally affected. Instead spend the ten minutes before an exam reviewing your past successes with math or other exams. Write down your concerns and thoughts, and then think about some positive reasons for why you will nail this exam, including running through some of the important ideas you have memorized. These strategies can prime your brain for optimal performance on the exam.
Don't struggle alone! You have many options for
with this course.
- Me. Feel free to come to my office hours,
make an appointment by email or phone, or simply try stopping by my
office—you are welcome whenever my door is open. If
you have some anxiety about taking math exams, please come see me and
we can work together on building your math confidence.
- Homework. Although the practice problems are not
graded, please work through them. Mathematics
is learned ACTIVELY, not passively. You
can't absorb math through listening or reading, even if you think you
understand it all.
- Textbook. I won't go over everything that is
contained in the text, and I will try to avoid doing the same examples. Hence your textbook in an important
independent source of information and you should read it!
- Lecture notes. Reviewing the notes you take in lecture
will give you a chance to see the material again after you have had
some time to assimilate it.
- Your classmates. Discussing math with others can help you
think through the concepts. Explaining an
idea you already understand will deepen your comprehension, and for the
concepts that you don't understand well, the explanation of a peer may
be more helpful than mine or the textbook's.
- Mathematica is available for all
college-owned computers, and is already installed in all of the public
labs, e.g. in on the first floor of Seeley Mudd. Mathematica
isn't available for student-owned computers for free, but you can access Mathematica by connecting remotely to the Unix servers remus or romulus via the Gnome Desktop (see https://www.amherst.edu/offices/it/help/software/unix/VNC and then https://cms.amherst.edu/offices/it/help/software/unix/gnome/node/23577).
To the Math 272 Homework Schedule