NATIONAL UNIVERSITY OF SINGAPORE

FACULTY OF SCIENCE

Department of Mathematics

Course Structure of MA2101 Linear Algebra II (2010/2011 Semester 2)

I. Aims/Objectives

1.  To develop creative, innovative and logic thinking, and

2.  To learn foundationally important a mathematical skill--Linear Algebra.

II.  Course Contents

1.  Vector spaces over a field (2 - 10)

2.  Vector subspaces (11 - 16)

3.  Linear spans and Direct sums of subspaces (17 - 29)

4.  Linear independence, Basis and Dimension (30 - 40)

5.  Row space and Column space (41-52)

6.  Quotient spaces and Linear transformations (53 - 66)

7.  Representation matrices of linear transformations (67 - 81)

8.  Eigenvalue and Cayley-Hamilton theorem (82 - 100)

9.  Minimal polynomial and Jordan canonical form (101 - 125)

10.  Quadratic forms, Inner product spaces and Conics (126-153)

III.  Prerequisites and requirements

1.  I will assume and use freely (mostly without proof) the results in Linearly Algebra I (e.g. the 7 Chapters book, written by S. L. Ma, V. Tan and K. L. Ng).

2.  HW1-5 should be slipped inside my office by Monday 6pm, of Weeks 3, 5, 8, 9, 11

(i.e., 24 Jan, 7 Feb, 7, 14 and 28 Mar, 2011).

3.  Late submission will not be accepted.

IV.  Recommended texts

1.  (Main Textbook) Stephen H. Friedberg, Arnold J. Insel and Lawrence E. Spence, Linear Algebra, Prentice Hall.

2.  Howard Anton (or with Chris Rorres), Elementary Linear Algebra (or Applications version), John Wiley & Sons.

V.  Mode of assessment

1.  To emphasize the importance of active learning and discussion during the tutorial, 10% of the final grade of a student will be contributed from his/her 5 Homework and average participation level over all tutorial sessions throughout the whole semester.

2.  Another 30% of the final grade will come from a 1-hour common test which will be held on Friday 4th March 2011 (tentatively), during the lecture time.

3.  The remaining 60% of the final grade will be from the semester examination scheduled in April / May 2011.

VI.  Contact Hours

2 Lectures (2 x 90min) + 1 Tutorial per student per week. Lectures will start from the week

10 – 14 January 2011. Tutorial sessions will start from the week 24 – 28 January 2011.

For office consultation, email me to make appointment. Email enquiry: anytime!

Lecturer: Zhang D Q (Professor)

Office: S17-#06-08-22, Department of Mathematics

E-mail: Tel. 6516-2795

Website: http://www.math.nus.edu.sg/~matzdq https://ivle.nus.edu.sg/default.aspx

2 January 2011