MCS 221, Linear Algebra
(11:30-12:20 MTuThF in OHS 318)

Syllabus: Here is the syllabus.

Office hours for the rest of the semester:

• 2:30-3:30, Tue, 5/21
• 10:30-12:30 and 3:15-4:30, Fri, 5/24
• 1-3, Mon, 5/27

Online resources:

• Summary of what we learned about operations, fields, and modular arithmetic.
• Introduction to complex numbers
• One of the supplementary textbooks for this course is A First Course in Linear Algebra, by Robert A. Beezer. You can also read the book in your browser or download a pdf that is better tailored for a tablet screen here.
• The other supplementary textbook is Linear Algebra Done Wrong, by Sergei Treil.
• Here is a brief paper by Wolf Holzman with an elegant proof of the uniqueness of the reduced row-echelon form of a matrix.
• Webwork is where you do your online homework. You cannot access Webwork from a computer off campus directly for security reasons. To access Webwork off campus, use Virtual Lab. Virtual Lab runs a virtual computer, which behaves much like a computer on campus, in a window on your own computer. You enter your usual Gustie username and password to login, and once the virtual computer boots up, run a browser in it and acccess the Webwork website through that browser.
• I use Moodle to post your grades periodically throughout the semester

Homework:

Assigned	Due	Read	Exercises
2/15	2/22	Operations, fields, and modular arithmetic.	Verify that the set of rational numbers with ordinary addition and multiplication is a field. Verify that Z7 is a field. Explain why Z10 is not a field. Let R[x] be the set of all polynomials with real coefficients. Define addition and multiplication of polynomials as usual. Is R[x] a field? Let S be the set of all functions from the real numbers to the real numbers. Define addition of f and g as (f+g)(x) = f(x) + g(x) and multiplication as (fg)(x) = f(x) g(x). Is S with this addition and multiplication a field?
2/22	3/1	Introduction to complex numbers, 1.A and 1.B in LADR	1.A.6, 8, 10, 11, 15. Full justification is expected. Don't forget about uniqueness in 1.A.8.
3/1	3/8	1.C	1.B.1-3, 5, 6
3/8		1.C, 2.A	Homework holiday. Review for the upcoming exam.
3/15	3/22	2.A	1.C.7, 8, 11 (try not to assume that the collection is finite), 17, 24 If you that know the difference between countable and uncountable sets, try doing 1.C.11 without assuming that the collection consists of countably many subspaces . If you know need some help with good notation for the intersection of infinitely many sets, feel free to ask.
3/22	3/29	2.A and 2.B	2.A.1, 3, 5, 6, 10
3/29	4/12	2.B and 2.C	2.A.11, 14, 16, 17 2.B.2
4/12		pp. 7-21 in First Course in Linear Algebra (posted above)	Homework holiday. Review for the upcoming exam.
4/18	4/26	pp. 22-32, 162-165, and 179-185 in First Course in Linear Algebra	2.B.4, 7 2.C.3, 9, 17
4/18	5/3		Webwork: HW0
4/26	5/3	pp. 58-65, 175-178 in First Course in Linear Algebra	Webwork: HW1 Offline: 2.C.16
5/3	5/10	pp. 45-54, 66-71, 193-204 (don't worry about Thm MIT) in FCLA; 3.A in LADR	Webwork: HW2 Offline: T11 and T13 in Section RREF of FCLA (p. 44)
5/10	5/17	3.A-C and 5.A in LADR	Webwork: HW3 Offline: 3.A.3, 8 and 3.B.11
5/17		5.A in LADR	Take a look at the following exercises. You don't need to turn them in, but thinking about them will help you practice the concepts we have recently covered. You can of course ask about them in office hours if you need help or a hint. 3.C.3, 7 and 5.A.7 (see example 5.8)

Exam solutions:

• First hourly exam pdf
• Second hourly exam pdf
• Final exam pdf

Educational links:

• A serious paper on teaching/learning at the university level by Prof. Steven Zucker
• A more light-hearted, but very true guide on how to be on good terms with your professor (who assigns your grade) by Prof. Doug Andrews at Wittenberg University

Math links:

• Our own Problems of the Month are an excellent way to hone your reasoning skills. Most, if not all, of these problems require no knowledge of advanced math beyond what you already know to be solved. You can even earn a prize by submitting your solutions.
• Wolfram MathWorld is an interactive math encyclopedia.
• Wolfram Alpha gives you access to many features of Mathematica, an extremely powerful computer algebra program, without paying $$$ and learning Mathematica syntax. It does not only do algebra.

Some scholarship opportunities for prospective teachers:

• Knowles Science Teaching Foundation