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Math 2210 Fall 2016 (Roby) Tom Roby's Math 2210Q Home Page (Fall 2016)
Applied Linear Algebra

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Class Information

COORDINATES: Classes meet Tuesdays and Thursdays 2:00-3:15 in MONT 225. The registrar calls this Section 002, #2698.

PREREQUISITES: MATH 1132, 1152, OR 2142.

TEXT: David C. Lay: Linear Algebra and Its Applications, 4th Ed., available in the bookstore. Let me know if you have any trouble getting it.

WEB RESOURCES: The homepage for this course is http://www.math.uconn.edu/~troby/math2210f16. The author also has a useful site with review sheets and downloadable data here.

SOFTWARE: In most areas of mathematics it is frequently helpful to use computer software not only for computations, but also to explore examples, search for patterns, or test conjectures. For linear algebra there are several extensive and sophisticated commercial software packages, including MATLAB, Maple, and Mathematica. Matlab is particularly good at linear algebra for applications. All of these can be expensive, depending on your site license.

An excellent alternative to the above is the free open-source computer algebra system Sage. There are many commands for linear algebra, and a textbook (linked below) has been written that makes significant use of Sage examples. Sage also provides a full-fledged programming environment via the Python programming language, but you don't need to be a programmer to use it. I highly recommend trying it out online, and installing a copy on your computer.

GRADING: Your grade will be based on two midterm exams, a final exam, homework, and quizzes.

The breakdown of points is:

Midterms Final Quizzes Homework
20% each 30% 20% 10%

EXAMS: The exam dates are already scheduled, so please mark your calendars now (midterms in class on 29 September and 1 November at the usual time; final TBD by registrar during the week of 12-16 December). All exams (like math itself at this level) are cumulative. No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage.

QUIZZES: Quizzes will be given each Thursday (except midterm exam days), covering (a) sections from the previous week (at the level of HW exercises) and (b) the reading assigned for the current week (at the level of True/False exercises). Your lowest two quiz scores will be dropped. Here is a sample Practice Quiz so you know ahead of time what the format will be. (Solutions will be provided below.)

HOMEWORK: Homework will be assigned most weeks, and is DUE at class the following TUESDAY. Since I may discuss the homework problems in class the day they are due, late assignments will be accepted only under the most extreme circumstances. Please let me know as soon as possible if you find yourself with a situation that might qualify. The lowest written homework score will be dropped in any event. I've color coded the schedule by week to help clarify what the HW is for a given week.

You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. More importantly, it is a poor learning strategy.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For quizzes and exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used unless otherwise specifically indicated on the exam.

CONTENT: Linear Algebra is a beautiful and important subject, rich in applications within mathematics and to many other disciplines. For many of you this is the first course to begin bridging the gap between concrete computations and abstract reasoning. Understanding the notions of vector spaces, linear (in)dependence, dimension, and linear transformations will help you make sense of matrix manipulations at a deeper level, clarifying the underlying structure.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

We will often spend classtime doing things in groups, presenting mathematics to one another, or having interactive discussions. There will not be time to "cover" all material in a lecture format so you will need to read and learn some topics on your own from the book (or otherwise).

SCHEDULE: I will update the following schedule over the course of the semester. Generally we will cover three sections per week, which means splitting a section between two lectures. Lecture notes are linked section by section: I recommend you review them before or after lecture, allowing you to spend lecture time focussing on the material rather than copying things down. If you have a religious observance that conflicts with your participation in the course, please meet with me within the first two weeks of the term to discuss any appropriate accommodations.

I've color coded the schedule by week to help clarify what the HW is for a given week.

2210Q LECTURE AND ASSIGNMENT SCHEDULE
Section Date Topics HW Problems
§1.1 8/30 T Intro to Linear Alg & Systems of Eqns. 1, 2, 3, 10, 12, 13, 15, 16, 21, 24, 25, 31, 32
§1.2 9/1 R Row Reduction & Echelon Forms 2, 10, 13, 14, 19, 21, 24, 29, 31
§1.3 9/1 R Vector Equations 3, 6, 7, 9, 12, 14, 15, 21, 22, 23, 25
§1.4 9/6 T Matrix Equations 1, 4, 7, 9, 11, 13, 17, 19, 22, 23, 25, 31
§1.5 9/8 R Solution Sets of Linear Systems 2, 6, 11, 15, 18, 19, 22, 23, 27, 30
§1.7 9/13 T Linear Independence

1, 2, 5, 7, 9, 15, 16, 20, 21, 32, 35

§1.8 9/13 T Linear Transformations

2, 4, 8, 9, 13, 15, 17, 21, 26, 31

§1.9 9/15 R Matrix of Linear Transformation

1, 2, 5, 13, 15, 20, 23, 26, 32, 34

§2.1 9/20 T Matrix Operations and Inverses

2, 5, 7, 10, 15, 20, 22, 27, 28

§2.2 9/22 R Inverse of a Matrix

3, 6, 7, 9, 11, 13, 15, 23, 24, 29, 32, 37

§2.3 9/22 R Characterizations of Invertible Matrices

1, 3, 5, 8, 11, 13, 15, 17, 26, 28, 35, 40(challenge!)

Ch. 1 9/27 T Supplementary Exercises

6, 7, 10 ,18, 22, 23

§3.1 9/27 T Intro to Determinants

4, 8, 11, 13, 20, 21, 31, 32, 37, 39

§3.2 9/27 T Properties of Determinants

2, 3, 8, 10, 16, 17, 20, 26, 27, 32, 34, 40

§3.3 9/29 R Cramer's Rule & Volumes

4, 5, 6, 22, 23, 26, 29, 30;

§1.1–2.5 10/4 T Catchup & Review Day Do Practice Midterm by today!
THURSDAY 6 OCTOBER: FIRST MIDTERM EXAM (through §2.3)
HW 3.1–3.3 and Chapter 1 Suppl. due on 10/13

§4.1 10/11T Vector Space & Subspaces

1, 3, 8, 12, 13, 15, 17, 22, 23, 31, 32

§4.2 10/13 R Null Spaces, Column Spaces & Lin. Transf.

3, 6, 11, 14, 17, 19, 21, 24, 25, 32, 33, 34, 36

§4.3 10/18 T Bases and Lin Ind. Sets

3, 4, 8, 10, 14, 15, 21, 23, 24, 29, 30, 31;

§4.4 10/20 R Coordinate Systems

2, 3, 5, 7, 10, 11, 13, 15, 17, 21, 23, 32

§4.5 10/25 T Dimension of a VS

1, 4, 8, 11, 14, 21, 23, 26, 28, 29

§4.6 10/25 T Rank

2, 5, 7, 10, 13, 19, 24, 27, 28;

§4.7 10/27 R Change of Basis

1, 3, 5, 7, 9, 11, 13, 15

§5.1 11/1 T Eigenvectors & Eigenvalues

2, 6, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 31

§5.2 11/1 T Characteristic Equation

2, 5, 9, 12, 15, 19, 20, 21

§5.3 11/3 R Diagonalization

1, 4, 5, 9, 11, 15, 17, 21, 24, 26

§5.4 11/8 T Eigenvectors & Linear Transformations

1, 3, 6, 7, 10 ,15, 16, 23, 25

§6.1 11/8 T Inner Product & Orthogonality

3, 5, 10, 16, 18, 19, 23, 25, 27, 29

§6.2 11/10 R Orthogonal Sets

3, 6, 8, 9, 11, 14, 20, 21, 23, 26, 27, 28, 29

§6.3 11/15 T Orthogonal Projections

1, 6, 7, 9, 11, 13, 17, 21, 23, 24

§1.1–5.2 11/15 T Catchup & Review Day Do Practice Midterm 2 by today
THURSDAY 17 NOVEMBER SECOND MIDTERM EXAM (through §5.3)
HW 5.4, 6.1 and 6.2 due on TUES 11/29; 6.3 due as usual on THURS 12/1.

25-29 NOVEMBER THANKSGIVING BREAK NO CLASSES
§6.4 11/29 T Gram-Schmidt Process

1, 3, 7, 9, 11, 17, 19

§6.5 11/29 T Least-Squares Problems

3, 5, 7, 9, 11, 17, 19, 21

§7.1 12/1 R Diagonalization of Symmetric Matrices

1, 3, 5, 8, 10, 13, 17, 19, 25, 29

§7.2 12/6 T Quadratic Forms

1, 5, 8, 11, 13, 19, 21, 27

§7.3 12/6 T Constrained Optimization

1, 3, 5, 7, 11

§7.4 12/8 R Singular Value Decomposition

1, 3, 9, 11, 17

THURSDAY 15 DECEMBER 3:30–5:30 FINAL REVIEW IN/NEAR MONT 225
SATURDAY 17 DECEMBER 10:30–12:30 FINAL EXAM IN MONT 225


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