Math 1553 Introduction to Linear Algebra Sections H & J Spring 2016

This is a basic, first course in linear algebra. The main goals are to understand matrices and systems of linear equations, to learn to solve problems from a mathematical perspective, and to prepare for the many applications of linear algebra in other science and engineering courses. Specifically objectives include:

• To learn to solve systems of linear equations through the use of matrices, including the methods of row reduction, inverse matrices, and LU decompositions.
• To understand the set of all solutions of a system of linear equations - with varying parameters - specifically through the parametric forms for solutions, the geometry of linear transformations, the characterizations of invertible matrices, and determinants.
• To learn to solve eigenvalue problems through the use of the characteristic polynomial.
• To use the computation of eigenvalues and eigenvectors to understand the structure of a linear transformation, for instance by diagonalization.
• To understand orthogonal projections and how they are used to find best-fit solutions to systems of linear equations that have no actual solution.

Instructor

Prof. Dan Margalit
Skiles 244
(404) 894-2715

Learning Assistants

Section H: Baishen Huang and Shivang Sullere
Section J: Scott Guan, Matthew Krumwiede, and Yashvi Shah

Class Meetings

Mondays, Wednesdays, and Fridays 11:05-11:55 (Section H) and 1:05-1:55 (Section J) in Clough 144.

Book

Students with a Pearson code can access the text via MyMathLab. The course id is margalit31057. Note: While the Pearson code is not required for this course, you are likely to need the code for other Math courses you take at GaTech, and so most likely buying the code now will save you money in the long run.

Office Hours

Prof. Margalit, Skiles 244 or 236, Tue 2-3, Wed 2-3, and by appointment

Scott Guan, Skiles 230, Mon 12-1
Yashvi Shah, Skiles 230, Mon 2-3
Baishen Huang, Skiles 230, Wed 4-5
Matt Krumwiede, Skiles 230, Thu 3-4
Shivang Sullere, Skiles 230, Tue 5-6

Math Lab

Drop-in help, Clough 280. The Math Lab will be strictly devoted to Math 1553 5:00-6:00 Monday through Thursday and 11:00-12:00 on Tuesdays and Thursdays. The Math Lab is also open for all classes Mondays and Wednesdays 11-5, and Tuesdays and Thursdays 12-5. Our Learning Assistants will be in the Math Lab at the following times:

Matt Krumwiede: Tuesday 11-12
Scott Guan: Tuesday 5-6
Baishen Huang: Thu 11-12
Yashvi Shah: Thu 5-6
Shivang Sullere: Thu 5-6

Homework

There are three forms of homework.

• Most homework will be assigned on WebWork, an online homework system accessible via TSquare. Online assignments will be due on Thursdays at 11:59 pm. Note that each week's assignment will consist of problems from 1-2 sections of the text (so they will look like multiple assignments online).
• The second form of homework will be written, and will consist of one problem per week, similar to an exam problem, and due on Friday at the start of class.
• The third type of homework will consist of two short papers on applications of linear algebra. The lowest homework grade will be dropped.

Quizzes

Quizzes will be given during each Friday that has no exam (except the first). Quizzes will be based on the homework and additionally serve as practice for exams. The lowest quiz grade will be dropped.

Participation

The course will use Piazza, available via TSquare, to perform classroom polling. Student scores are based solely on participation. The three lowest participation scores will be dropped.

Schedule

Week	Date	Sections	Topics and Course Notes	WebWork	Homework	Quiz/Exam
1	Jan 11		Overview
	Jan 13	1.1	Linear systems
	Jan 15	1.2	Row reduction	Warmup
2	Jan 18	Martin Luther King Day
	Jan 20	1.3	Vector equations
	Jan 22	Snow Day
3	Jan 25	1.4	Matrix equations	1.1,1.2	Written Homework 1	Quiz 1: 1.1,1.2
	Jan 27	1.5	Linear systems
	Jan 29			1.3, 1.4	Written Homework 2	Quiz 2: 1.3,1.4
4	Feb 1	1.7	Linear independence
	Feb 3	1.8	Linear transformations
	Feb 5		Worksheet 1	1.5	Written Homework 3	Quiz 3: 1.5
5	Feb 8	1.9	Matrix of a linear transformation
	Feb 10		Review			Practice 1
	Feb 12	Chapter 1	Linear equations	1.8,1.9		Exam 1
6	Feb 15	2.1,2.2	Matrix Algebra / Inverses
	Feb 17	2.3	Invertible matrices
	Feb 19		Worksheet 2	2.1, 2.2	Written Homework 4	Quiz 4: 2.1, 2.2
7	Feb 22	2.5	LU decomposition
	Feb 24	2.8	Subspaces
	Feb 26			2.3, 2.5	Written Homework 5	Quiz 5: 2.3, 2.5
8	Feb 29	2.9	Dimension and rank
	Mar 2	3.1	Determinants
	Mar 4			2.8, 2.9	Written Homework 6	Quiz 6: 2.8, 2.9
9	Mar 7	3.2	Properties of determinants
	Mar 9		Review			Practice 2
	Mar 11	Chapters 2-3	Matrix algebra	3.1, 3.2		Exam 2
10	Mar 14	5.1	Eigenvectors
	Mar 16	5.2	Characteristic polynomial
	Mar 18		Worksheet 6	5.1	Written Homework 7	Quiz 7: 5.1
	Mar 21	Spring break
	Mar 23	Spring break
	Mar 25	Spring break
11	Mar 28	5.3	Diagonalization
	Mar 30	5.5	Complex eigenvalues
	April 1			5.2, 5.3	Written Homework 8	Quiz 8: 5.2,5.3
12	Apr 4	5.5	Complex eigenvalues
	Apr 6		Review			Practice 3
	Apr 8	Chapter 5	Eigenvectors	5.5		Exam 3Exam 3
13	Apr 11	6.1	Inner products
	Apr 13	6.2,6.3	Orthogonal projections
	Apr 15	Worksheet 9		6.1, 6.2	Written Homework 9	Quiz 9: 6.1, 6.2
14	Apr 18	6.4	Gram-Schmidt and QR
	Apr 20	6.5	Method of least squares
	Apr 22	Worksheet 10		6.3, 6.4	Written Homework 10	Quiz 10: 6.3, 6.4
15	Apr 25		Review	6.5		Practice Final
16	May 2	Cumulative	Linear algebra			Final Exam Sec J, 2:50-5:40
	May 4	Cumulative	Linear algebra			Final Exam Sec H, 8:00-10:50

Grading

Final grades will be computed according to the following scale:

Participation 5% Quizzes 10% Homework 10% Midterms 45% Final Exam 30%

The final exam score may be used to replace half of the lowest midterm score.

Absences

As a general rule, absences are excused for official Georgia Tech business only. I reserve the right to ask for a letter from the Dean of Students. If you have an official excuse for absence for an exam, you will be excused from that exam without penalty, meaning that your other exams will count for a larger portion of your grade.

Devices

Please do not use electronic devices during class for activities that are not related to class.

Resources

---Math 1553 HP Fall 2015

---Course notes Fall 2015

---Prof. Grodzinsky's Review Sheet

---Determinants

---Complex Eigenvalues and Factorization

---T-Square

---Math Lab, in Clough 280.

---Center for Academic Success, Drop in tutoring and one-on-one tutoring

---ADAPTS, Disabilities Services Program

---Honor code