Math 1180:      Linear Algebra        Fall 2014

Instructor: David Swigon

Office: Thackeray 511, 412-624-4689, swigon@pitt.edu

Lectures:  MWF 9:00-9:50am, Thackeray 704

Office Hours: MWF 10:00-11:30am, Thackeray 511, or by appointment.

Grader: Roxana Tanase, rot26@pitt.edu, office hours Monday 5-7pm, Friday 9-11am, at MAC

Web Page: http://www.math.pitt.edu/~swigon/math1180.html

Course Description

This is a core undergraduate course in linear algebra and matrix analysis for mathematics majors. The emphasis will be placed on the understanding of concepts and their application in further development of the theory. Specifically, the course covers topics such as solutions of linear equations, matrix algebra, linear transformations, orthogonality, general linear vector spaces, basis, dimension, eigenvalues/eigenvectors. The grade will be based on evaluation of both problem solving and theorem proving skills.

Prerequisites

Multi-variable Calculus (Math 0240 or equivalent), and familiarity with solving of systems of linear equations. Introduction to Theoretical Mathematics (Math 0413 or equivalent).

Textbook

D. Poole , Linear Algebra; a Modern Introduction, 2nd edition, Brooks & Cole, 2006. ISBN 0-534-40596-7

Grading Scheme

Homework Assignments: 20%
Two midterm exams: 40% (20% each)
Cumulative Final Exam: 40%

Schedule

The precise schedule and a list of homework problems will be given out in advance and posted on the web. Homework is assigned every Friday and is due at the beginning of a class one week after it was assigned. You MAY NOT use a computer or other electronic tools in solving the homework unless I specifically say otherwise.

Policy

Attendance is expected.  No late homework will be accepted and there will be no make up exams.

Disability Resource Services

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

Academic Integrity

Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.


Schedule

Please note that the schedule is approximate and the pace and/or order of the topics may change during the semester.

LECTURE

CHAPTERS

TOPICS

HOMEWORK ASSIGNED

Due Friday the week after

(numbers in parentheses refer to the 3rd edition of the textbook)

Aug 25 - Aug 29

1.1-1.2

1.3

2.1

Geometry and algebra of vectors, length and angle, dot product

Lines, planes, cross product

Systems of linear equations, Row echelon form

Chap 1.2 #17, 30, 37(43), 44(50), 50(56), 56(62)

Chap 1.3 #4, 8

Chap 2.1 #8, 17

Due Sep 5

Solutions

Sep 1

Labor Day (no school)

 

Sep 3 - Sep 5

2.2

2.3

Gaussian elimination

Spanning sets & linear independence

Chap 2.2 #13, 18, 21, 30, 38, 49, 50

Chap 2.3 #8, 12

Due Sep 12

Solutions

Sep 8 - Sep 12

2.3

2.4

Spanning sets & linear independence

Application: Resource allocation, Network Analysis

Chap 2.3 #21, 24, 27, 30, 43

Chap 2.4 #2, 5, 17

Due Sep 19

Solutions

Sep 15 - Sep 19

3.1-2

3.3

Matrices, matrix operations, Matrix algebra

Matrix inverse

Chap 3.1 #14, 23, 24, 28, 30, 38

Chap 3.2 #20, 27

Chap 3.3 #2, 9, 12

Due Sep 26

Solutions

Sep 22 - Sep 26

3.5

Subspaces, bases, dimension, rank

Chap 3.3 # 43, 47, 52, 55

Chap 3.5 # 2, 6, 12, 18, 29, 40, 44, 57(59)

Due Wednesday Oct 1

Solutions

Sep 29 Oct 1

3.7

Applications: Markov chains and graphs

Review

Exam review sheet

Sample exam

Sample exam solutions

Oct 3

Exam I

Solutions

Oct 6 - Oct 10

4.1

4.2

Introduction to eigenvalues and eigenvectors

Determinants

Chap 3.7 # 5-8, 12

Chap 4.1 # 3, 6, 9, 14, 23, 26, 35, 36

Chap 4.2 # 6, 12, 33, 38, 46, 49, 55

Due Oct 17

Solutions

Oct 13

Fall Break (no school)

 

Oct 14 Oct 17

4.3

4.4

Eigenvalues and eigenvectors of n x n matrices

Similarity and diagonalization

Chap 4.3 # 2, 5, 9, 17, 18,19, 20, 24

Chap 4.4 # 2, 4, 10, 11

Due Oct 24

Solutions

Oct 20 Oct 24

4.4

4.6

Similarity and diagonalization

Applications: Recurrence relations, Systems of linear differential equations

Chap 4.4 #12, 17, 28, 34, 43, 44

Chap 4.6 #45(47), 47(49), 53a-b(55a-b), 58(60)

(numbers in parentheses refer to the 3rd edition of the textbook)

Due Oct 31

Solutions

Oct 27 Oct 31

5.1

5.2

Orthogonality

Orthogonal complements and projection

Chap 5.1 #3, 5, 10, 13, 19, 23, 30, 35

Chap 5.2 #4, 13, 16, 21, 27

Due Nov 7

Solutions

Nov 3 Nov 7

5.3

5.4

Gram-Schmidt process

Orthogonal diagonalization of symmetric matrices

Chap 5.3 #4, 7, 10, 12, 13

Chap 5.4 #2, 7, 24, 25

Due Wednesday Nov 12

Solutions

Nov 10 - Nov 12

Application: Quadratic forms

Review

Exam II review sheet

Sample exam II

Sample exam II solutions

 

Nov 14

Exam II

Solutions

 

Nov 17 Nov 21

6.1

6.2

Vector spaces and subspaces

Linear independence, basis, dimension

Nov 24

6.2

Basis, dimension

 

Dec 1 - Dec 5

6.4

6.5

Linear transformations

Kernel and range of a linear transformation, Invertibility of a linear transformation

Review for final exam

Additional review sheet

Chap 6.1 #3, 5, 33, 36

Chap 6.2 #4, 14, 23, 27, 37

Chap 6.4 #3, 10, 16, 22

Chap 6.5 #3, 12, 17, 20

Due Friday Dec 5

Solutions

Tuesday

Dec 9

 

FINAL EXAM

4:00 - 5:50 pm

THACK 704