Math 217: Linear Algebra Section 3
Winter 2017

Professor Karen E. Smith

The Amazing Section 3

Math 217 is a first course in linear algebra with proofs. In addition to learning linear algebra, a main goal of the course is to teach students how to make a rigorous mathematical argument.

This the Section 3 webpage. Students in Section 3 should be regular users of both the Canvas site (joint for all sections) and this site.

SYLLABUS: Here (but always check Canvas for the official, possibly more updated, version.)

DAILY UPDATE: Section 3 Daily Update summarizing classroom actitivies, assignments and quiz announcements.

REQUIRED READING:

Linear Algebra with Applications, textbook by Otto Bretscher (fifth edition).
The Joy of Sets
Mathematical Hygiene
Definitions and Theorems in Book Order, supplement on the theoretical aspect of linear algebra, including rigorous definitions and proofs.
Proof Technique Document, a summary of some common techniques to get started on proofs.
Coordinate Change and All That, Mysteries of 3.4 and 4.3 revealed.
Definitions and Theorems for Exam 2
Eigen-Everything,

Definitions and Theorems for the Final,

Prove/Disprove Practice for Final, and the answers.

VIDEO ON GRAM-SCHMIDT PROCESS from Khan Academy: Sal Khan explains the Gram-Schmidt process (from 5.2 in the textbook) pretty well. In the video, he starts with "V" some SUBSPACE OF R^n, just like in the text. Actually, the entire series in this section of Khan Academy (called "Linear Algebra > Alternate Coordinate Systems" starting with "Introduction to Orthonormal Bases" and ending with "Gram-Schmidt Process with 3 basis elements" is pretty good and uses more or less the same notation we do in Chapter 5.

WORKSHEETS:
Jan 4 on Systems of Linear Equations (1.1), Jan 6 on solving systems and row reduction (1.2), Jan 9 (more on linear equations), Jan 11 on Linear Combinations (1.3), Jan 13 on Linear Transformations (2.1), Jan 18 on Projections and Reflections (2.2), two worksheets on Jan 20: Compositions of Linear Transformations (2.3) and Inductive Proof Practice, Jan 23 on the geometric meaning of the determinant, January 25 on Injective, Surjective and Bijective Transformations (2.4) (and with Answers) (also and here is the original version if you need it), Jan 27 on Vector Spaces (4.1), January 30 on Span, Kernel, Image (3.1), February 1 on Linear Independence (3.2), February 3 on Subspaces and Bases (3.2 3.3), February 6 and Februrary 8 on Bases (3.3, 4.1, 4.2), February 10 on Coordinates (3.4, 4.3), February 13 on Coordinates, part 2 (3.4, 4.3), February 17 and Feb 20 on Modelling with Coordinates (4.3) and a similar worksheet used Feb 20 Changing Coordinates and the B-matrix (4.3), Worksheet from Feb 22 on Non-Standard Basis (3.4 and 4.3), Worksheet from Feb 24 on Orthonormality (5.1), Worksheet from March 6 on Orthogonal Projection, Gram-Schmidt (5.1 and 5.2), Worksheet from March 8 on QR Factorization (5.2), Worksheet from March 10 on Orthogonal Transformations (5.3), Worksheet from March 13 on Least Squares (5.4), Worksheet from March 15 and March 17 on Inner Product Spaces (5.5), March 20 on Determinants (6.1) March 22 on , Geometric Meaning of Determinants (6.2), March 24 on Alternating and MultiLinear Properties of Determinants (6.3), March 27 on Proofs of Determinant Theorem and Group Quiz 6, March 31 on Eigenvalues and Eigenvectors, April 3 on Eigenspaces and the Characteristic Polynomial, April 5 on Finding Eigenvalues and their Multiplicities, April 7 on More on Multiplicities, April 10 and 12 on Eigen Practice, April 12 on Spectral Theorem, April 14 on Proof of the Spectral Theorem, April 17 on Rotations in Three-Space, and Prove/Disprove Practice for Final, and the answers.

Extra Worksheets on: Elementary Matrices (chapter 1), Geometry of Linear Maps (chapter 2), Using Linear Algebra to Prove Trig Formulas (chapter 2), Rank Nullity Practice (chapter 3), Fourier Coefficients and Approximating Functions (chapter 5) Application of Eigenvalues to Fibonnaci Sequence (chapter 7) Eigenvectors and Geometry in 3-space (chapter 7)

Answers to TF Questions in Chap 1 and 2 ("no" means we didn't cover that topic).
Answers to TF Questions in Chap 3 and 4

Group Quizzes and Quizzes:
Jan 6 Group Quiz on introduction to proofs, Quiz 1 Quiz 2 Quiz 3, Quiz 4, Group Quiz from Feb 1, Quiz 5, Group Quiz 3 from Feb 10, Quiz 6 from Feb 13, Group Quiz 4 from Feb 15, Quiz 7 from Feb 22, Quiz 8 from March 8 (and Alternate for folks who want a Re-do), from March 13 (corrected) Quiz 9, Group Quiz 5 from March 15, Quiz 9 Redux from March 20, Group Quiz 6 from March 27, Quiz 10 from April 3, Quiz 11 from April 10, Group Eigen Quiz 6 from April 14, Quiz 12 from April 17,

OFFICE HOURS: Mondays 3-5 in 3074 EH. Wednesday 11:30-12:30 in B735 EH.
You can (and should!) attend any Math 217 instructor's office hours. All hours are posted in Canvas.

COURSE EXPECTATIONS: Math 217 is a NON-LECTURE course. This means students are responsible for learning the material on their own through individual reading of the textbook working through more theoretical concepts in small groups using worksheets in class, working through more computational exercises using online web problem set (due wednesdays), and completing two written problem sets every week (one more computational, one on proofs) posted every Friday on canvas. Students should keep current on Canvas and on this website for assignments, announcements, due dates, etc. We also have a QUIZ every Monday, a Gateway Exam in week 3 (in the mathlab), two evening midterm exams and a Final. See Canvas for locations, time and more details on all exams. Students must carefully do the independent READING before each class, as I will not lecture on it . Usually, the reading will be tested by a brief online webwork "Reading Quiz" due by 8 am each Monday, Wednesday and Friday.

Most students find this a very challenging course, especially those who have never done "proofs" before. In order to succeed, it is crucial to do all reading both before class, and again after to ensure full understanding, complete webwork as soon as possible as it is assigned, start early on weekly problem sets, and get help from me or any other 217 instructor as soon as you need it.

Other Options: Math 417 and Math 214 both cover similar material from the same book. Math 417 is the most straightforward: it just covers the book material. Math 214 supplements the book material with many interesting applications. Math 217 supplements the book with more theory (and proofs).

I am available also by appointment if you need me and can't make regular office hours.

In addition, you can get help in the Math Lab whenever it is open.

All sections of Math 217 follow the same syllabus, take the same midterm and final exams, have the same online-webwork and weekly written assignments, and have the same grading scheme. There are, however, some minor differences between sections. In ours, for example, ATTENDENCE IS REQUIRED. Also, Section 3 students are expected to check the Daily Update every day, which will usually let you know when a quiz is coming and the reading assignment. No make up quizzes will be given (barring extreme situations--talk to me); however, your lowest two scores will be dropped.

Testing and Disability: If you think you need an accommodation for a disability, please let me know as soon as possible. In particular, a Verified Individualized Services and Accommo dations (VISA) form must be provided to me at least two weeks prior to the need for a test/quiz accommodation. The Services for Students with Disabilities (SSD) Office (G664 Haven Hall; http://ssd.umich.edu/ ) issues V ISA forms.

My Math Autobiography

Websites from Previous Semesters of Math 217
Winter 2016,   Fall 2015