Math 22: Linear Algebra with Applications
 FALL 2016
Section 1: Alex Barnett

Section 2: Naomi Tanabe

lectures: M,W,F 12:501:55pm (12 slot), Kemeny 007
 lectures: M,W,F 2:103:15pm (2 slot), Kemeny 105

Xhour: Tu 1:202:10pm (12X slot)
 Xhour: Th 1:202:10pm (2X slot)

office hours: M 56, Tu 56, F 11:30a12:30p (office Kemeny 206)
 office hours: M 3:454:45, Tu 1:302:30, F 12 (office Kemeny 315)

(Any Barnett extra material will appear on the below syllabus page)
 (Any Tanabe extra material will appear on the course's Canvas page)

Graduate teaching assistant: Yitong ("Pepper") Huang.
Her tutorials are: Sun,Tu,Th, 79pm in Kemeny 105.
Iterative convergence of PageRank vector in model of Google's search algorithm
(courtesy of D Austin / AMS)

About this course.
You all remember solving two simultaneous equations for two unknowns
in high school.
Linear algebra is the elegant structure that arises when you generalize
this to many equations in many unknowns.
We will find such algebra problems (involving numbers and matrices)
can be beautifully
described by geometry (involving planes and angles).
Goals of this course include: knowing the theory and practice of solving
any linear system you could come across, including learning some methods
of rigorous proof.
Why is linear algebra useful?
The natural and technological world around us is full of complicated
systems that respond
to stimuli: a bridge moves when a force is applied, the population of
one species reacts to a change in population of another. Very often the
system is linear (or nearly so)  twice the input causes twice the output  this is why linear algebra is everywhere.
Every time we do a web search, make a weather prediction, solve
virtually any numerical
problem in physics, chemistry, biology, engineering, economics,
we (or a computer!) does linear algebra.
Every molecule of your body is governed by quantum mechanics, which is
essentially linear algebra combined with complex numbers.
Anywhere your careers take you in science, engineering, or analytics,
you will need to solve linear systems  it is key to understand whether a solution is unique, or even exists.
Amazingly, linear algebra, particularly the idea we introduce of a
vector space,
can be generalized to infinite dimensions (don't worry  that's not in this course!) to create
the beautiful area of functional analysis
(the study of operators on functions,
a cornerstone of analysis, partial differential equations, etc).

Required book: Linear Algebra and Its Applications, Fourth Edition by David C. Lay
(Published by Addison Wesley).
This is a wonderful book that will serve you well in your careers.
Copies have been preordered at
Wheelock Books; if they run out do order online, etc.
Please make sure you have the 4th edition otherwise problem or section numbers may not match up.
Homework. This has two parts:
 For each lecture here we assign ungraded practice problems from the book, where most of your
study time will go. Doing these is essential to survival in the course!
We strongly recommend you work through these before the next lecture, to
cement your learning. If you can do these problems, you should have grasped
most material.
 Each Friday we will post here in PDF format
a set of around
three written problems which are to be handed in at the start of the following
Wednesday's lecture. (The 9th and last one will be shorter and due Monday.)
You should only do these once you have understood your practice problems, otherwise it's a waste of your time.
These problems will have space for you to write, will be graded carefully,
and are designed to be similar to exam questions to help train you for exams
(which comprise the other 80% of the grade).
Please make your working/reasoning as clear as you can, write clearly,
and staple your work.
Late homework will not be accepted.
On the other hand, your lowest graded HW score will be dropped (ie you get a "free" HW).
Together, these two parts of the homework will cover all material,
apart from occasional information about Matlab, which is "bonus" material.
Exams: We will try to give you ample time to complete exam
questions. "Cheat sheets" and calculators will not be allowed, and there will be no needs for them. Key is to practise problems and old exam questions until you are fluent (see this).

Midterm 1: Monday Oct 10, 68pm, Steele 006.

Midterm 2: Wednesday Oct 26, 68pm, Silsby 028.
(Note the choice of early date allows you to make a drop decision after
getting back your score.)

Final: Friday November 18, 11:30am2:30pm, LSC 100.
This is the joint math exam slot, hence the only way there can
be a conflict is if you are taking another multisection math course this Fall.
Please let us know.
Here's a quote that Prof Orellana uses that we really like:
"Mathematics is not for spectators; in order to gain in understanding, confidence, and enthusiasm one has to participate." M.A. Armstrong
Honor principle. Exams: no help given or received by any
means optical, auditory, electronic, olfactory, telepathic, etc.
Homework: group
discussion and collaboration on practice problems, and problem
techniques, is encouraged. The graded work you hand in must be done
individually and written up individually (ie no copying).
Grade scheme:
Your overall grade is computed via: HW 20%, Midterms 22.5% each, Final 35%.
Thus it's mostly exams, so you must become fluent and reliable
(see above quote)!
However, HW is the main chance you get to practise the material
and get feedback, so stay on top of it.
Grades in Math 22 are not curved; other students' good performance
will not hurt your grade, so please work together and help each other out!
Special needs: We encourage students with disabilities,
including "invisible" disabilities like chronic diseases and learning
disabilities, to discuss with us any appropriate accommodations that
might be helpful, in conjunction with your undergraduate dean.
Let us know asap, certainly in the first 2 weeks. Also
stop by the Academic Skills Center in 301 Collis to register for
support services.
Private tutoring:
The
Tutor Clearinghouse most likely has
oneonone tutors available for Math 22. The tutors are recruited on
the basis that they have done well in the subject, and are trained by
the Academic Skills Center. If a student receives financial aid, the
College will pay for three hours of tutoring per week.
Religious observance:
Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.