** 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.

Websites from Previous Semesters of Math 217

Winter 2016,
Fall 2015