Course Outline (Due dates are tentative)

MATH 273– Linear Algebra with Applications (Section 2L)

Spring 2014

Class Times:

Lectures: Tuesday, Thursday – 09:00 – 10.15 pm, Room #7105 (Section 2L)

Lab Sessions: Wednesday – 11:00 – 11:50 am, Lab #8322 (Section 2Lb)

                   Wednesday – 2:00 – 2:50 pm, Lab #7322 (Section 8Lb)

Instructor:GalymAkishev

Office: #7220

Office hours:M – 9.00 am – 10.15 am, 2.00 pm – 3.50 pm, W – 9.00 am – 10.15 am, F – 3.00 pm – 3.50 pm

or

by appointment

Phone:70-65-70

Email:gakishev@nu.edu.kz

Information about TAs: TBA

Pre-requisite: MATH 161 Calculus I with minimum passing grade C-.

Co-requisite: MATH 162 Calculus II.

Course Overview

This course is a one-semester course intended for mathematics, engineering, and science students. It introduces students to the fundamental concepts of linear algebra. The course will basically involve two mathematical objects: matrix and vector. Students will learn how to reformulate some mathematical problems into a form that involves these objects, to operate on them, to interpret them, and to characterize them. The course also exposes students to proofs of some algebraic properties of matrices. Some computational algorithms of practical importance are also discussed. As linear algebra has become an indispensable component in scientific computing, students will also learn how to use computational software (in this case, MATLAB) to solve problems that involve matrices and vectors.

Course Objectives

Students who successfully complete the course will:

· understand types of solutions of systems of linear equations

· understand row echelon forms

· be able to perform Gaussian elimination

· be able to do matrix operations: summation, multiplication, transposition

· know properties of (non)invertible matrices and properties related to (non)invertible matrices

· be able to compute the inverse of invertible matrices

· know the properties of the determinant and be able to compute the determinant

· be able to perform basic operations that involve vectors: dot product, cross product

· be able to characterize vector spaces

· be able to compute the orthogonal bases of a vector space via Gram-Schmidt process

· understand eigenvalues and eigenvectors and be able to compute them

· know diagonalization of matrices

· understand the relation between matrices and linear transformations

· be able to use MATLAB as a computational tool.

Course Materials

Main textbook:

David C. Lay, Linear Algebra and Its Applications, 4^th edition (International Edition), Pearson ISBN:978-0-321-62335-5.

Recommended for additional reading:

H. Anton, C.Rorres, Elementary Linear Algebra, 10^th edition, John Wiley and Sons, 2011. ISBN: 978-0-470-56157-7.

Course Assessment

Activity	Tentative Dates	Weight	Relevant SLOs
Midterm Exam 1	February 13, 2014 (Thursday)	25%	System of linear equations, row reduction and echelon forms, vector equations, the matrix equation Ax=b, solution sets of linear systems, applications of linear systems, linear independence, introduction to linear transformations, the matrix of a linear transformation, matrix operations, the inverse of a matrix, characterizations of invertible matrices, partitioned matrices, matrix factorizations
Midterm Exam 2	April 3, 2014 (Thursday)	25%	Subspaces of , dimension and rank, determinants, properties of determinants, Cramer’s rule, vector spaces and subspaces, null spaces, column spaces, linear transformations, linearly independent sets, bases, coordinate systems, the dimension of a vector space, rank, change of basis, eigenvectors, eigenvalues, the characteristic equation, diagonalization, linear transformations, complex eigenvalues
Final Exam	Final examination period (May 2 – May 12, 2014)	35%	System of linear equations, row reduction and echelon forms, vector equations, the matrix equation Ax=b, solution sets of linear systems, applications of linear systems, linear independence, introduction to linear transformations, the matrix of a linear transformation, matrix operations, the inverse of a matrix, characterizations of invertible matrices, partitioned matrices, matrix factorizations, subspaces of , dimension and rank, determinants, properties of determinants, Cramer’s rule, vector spaces and subspaces, null spaces, column spaces, linear transformations, linearly independent sets, bases, coordinate systems, the dimension of a vector space, rank, change of basis, eigenvectors, eigenvalues, the characteristic equation, diagonalization, linear transformations, complex eigenvalues, discrete dynamical systems, applications to differential equations, inner product, length, orthogonality, orthogonal sets, orthogonal projections, the Gram-Schmidt process, least-squares problems, applications to linear models, diagonalization of symmetric matrices, quadratic forms
Quizzes (there will be at least four quizzes)	TBA	10%	TBA
Lab Reports	Every week	5%	TBA

Note: All dates are subject to change.

Homework will be assigned every week. Homework assignments will not be collected and graded.

There are no make-ups or deferrals for the midterm tests and quizzes.

Grading criteria:

A     92-100

A-    90-91

B+   88-89

B     82-87

B-    80-81

C+   78-79

C     72-77

C-    70-71

D+   68-69

D     60-67

F     <60

Rounding: All grades will be rounded according to the standard rules for rounding.

Course Policies

Academic honesty

Any plagiarized paper, assignment, and/or exam will receive a score of 0 (zero).

Attendance policy

Students are expected to attend all classes (including lab sessions).

Tardiness policy

Any student, who is late for 10 minutes without any prior notification, will not be allowed to participate in a lecture or a lab session.

Class participation

Students are expected to actively and positively participate in this class.

Classroom decorum

The Instructor expects that students:

1) Arrive on time for class (instructors have the right to refuse entry to late-arriving students).

2) Notify the instructor if there is a legitimate need to leave class early.

3) Turn off all mobile phones and electronic devices

4) Refrain from talking to other students except during structured classroom activities (instructors have the right to direct offending students to leave the classroom).

5) Refrain from making disruptive noises such as slamming doors.

6) Behave in a respectful manner towards the instructor and other students (Incidents of insulting behavior and/or use of offensive language or gestures can be forwarded to a disciplinary committee for sanctions).

7) Show respect for opinions and beliefs of others even if there is disagreement.

Missed exams

All missed tests will be assigned zero, but the instructor will replace up to one missed test with the grade earned on the final, if the student has a valid excuse for missing the test (as determined by the Administration of SST).

Late assignments

No late assignments will be accepted.

Appeals policy

If a student believes that he or she has received an unfair or erroneous grade, the student may appeal. The student must first consult with the instructor within 10 working days of his or her receipt of the contested grade (that time may be extended in the event the instructor is shown to have been unavailable during the period following the student’s receipt of the grade in question). In the event that the student is still dissatisfied, he or she may appeal to the Dean of the relevant School or the Dean’s designee within 7 days. The Dean or designee shall consult with the Instructor before making any decision. The decision of the Dean or designee shall be final.

Electronic resources

You are expected to regularly check your Nazarbayev University email for updates and announcements about the course. You are also required to use Moodle as determined by the instructor.

MATLAB Sessions

MATLAB is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications.

From the point of view of the course, MATLAB has to be considered as a tool, which helps students to avoid routine arithmetic calculations so that students can focus on new concepts.

As an introduction to MATLAB, students may use the followinglinks:http://www.mathworks.com/products/matlab/examples.html (specifically look at “Basic Matrix Operations”)

http://www.mathworks.com/products/matlab/videos.html

Course Outline (Due dates are tentative)

Add deadline: January 15, 2014

Drop deadline: January 22, 2014

Withdrawal deadline: February 21, 2014

Week	Dates	Topics	Text chapters, reading materials, etc.
1	January 8(Wednesday) – January 10	System of linear equations, row reduction and echelon forms	Section 1.1, 1.2
2	January 13 – January 17	Vector equations, the matrix equation Ax=b, solution sets of linear systems	Section 1.3, 1.4, 1.5
3	January 20 – January 24	Applications of linear systems, linear independence, introduction to linear transformations	Section 1.6, 1.7, 1.8
4	January 27 – January 31	The matrix of a linear transformation, matrix operations, the inverse of a matrix	Section1.9, 2.1, 2.2
5	February 3 – February 7	Characterizations of invertible matrices, partitioned matrices, matrix factorizations	Section2.3, 2.4, 2.5
6	February 10 – February 14	Subspaces of , dimension and rank Midterm Exam 1	Section2.8, 2.9
7	February 17 – February 21	Determinants, properties of determinants, Cramer’s rule	Section3.1, 3.2, 3.3
8	February 24 – February 28	Vector spaces and subspaces, null spaces, column spaces, linear transformations, linearly independent sets, bases	Section 4.1, 4.2, 4.3
9	March 3 – March 7	Coordinate systems, the dimension of a vector space, rank	Section 4.4, 4.5, 4.6
10	March 10 – March 14	Change of basis, eigenvectors, eigenvalues, the characteristic equation	Section 4.7, 5.1, 5.2
11	March 17 – March 21	Diagonalization, linear transformations, complex eigenvalues	Section5.3, 5.4, 5.5
	March 24 – March 28	Spring Break
12	March 31 – April 4	Discrete dynamical systems, applications to differential equations Midterm Exam 2	Section5.6, 5.7
13	April 7 – April 11	Inner product, length, orthogonality, orthogonal sets, orthogonal projections	Section6.1, 6.2, 6.3
14	April 14 – April 18	The Gram-Schmidt process, least-squares problems, applications to linear models	Section6.4, 6.5, 6.6
15	April 21 – April 25	Diagonalization of symmetric matrices, quadratic forms	Section 7.1 (optional), 7.2 (optional)
16	April 28 – April 30(Wednesday)	Review	Review

Tips for success:

Solve as many problems as you can. Your answers have to coincide with answers in the textbook.