The University of Massachusetts Boston

Department of Mathematics

MA 260 Linear Algebra, Spring 2022

Instructor: Prof. Alfred Noël

Office : : 3-154-14 Wheatley

Phone : (617)-287-6458

Email : alfred.noel@umb.edu

Url : http://www.math.umb.edu/~anoel

Class hours : TTh 5:30 PM - 6:45 PM 

Room: M-1-608

Office hours: T: 2:00 PM – 3:50 PM Th: 2:50 PM – 3:50 PM https://umassboston.zoom.us/j/96541633195

Text : Linear Algebra and its applications 5th Edition by Otto Bretscher Publisher Pearson 9780321796974

 

NO COMPUTERS NO CELL PHONES IN CLASS

 

Course Info: This is an introductory course in Linear Algebra, one of the most fundamental tools in Mathematics and Science. The students are expected to be mathematically mature enough to start dealing with concepts beyond Calculus. The goal of this course is to give to students a set of mathematical tools that they will need in order to pursue advanced studies in Mathematics, Physics, Chemistry, Engineering in particular and Science in general. Students who are concerned about their mathematical background should speak to me as soon as possible for advising. Students who have taken Calculus I, II should, in principle, be able to take this course. However, regardless of your background you will find the course to be very challenging. Consequently, you should not collaborate on homework and you should participate in class discussions. Also, I strongly advise students to form discussions groups that meet outside of the class-room. We will cover:

 

1 Linear Equations

1

(40)

1.1 Introduction to Linear Systems

1

(7)

1.2 Matrices, Vectors, and Gauss--Jordan Elimination

8

(17)

1.3 On the Solutions of Linear Systems; Matrix Algebra

25

(16)

2 Linear Transformations

41

(69)

2.1 Introduction to Linear Transformations and Their Inverses

41

(17)

2.2 Linear Transformations in Geometry

58

(17)

2.3 Matrix Products

75

(13)

2.4 The Inverse of a Linear Transformation

88

(22)

3 Subspaces of Rn and Their Dimensions

110

(56)

3.1 Image and Kernel of a Linear Transformation

110

(12)

3.2 Subspaces of Rn; Bases and Linear Independence

122

(11)

3.3 The Dimension of a Subspace of Rn

133

(14)

3.4 Coordinates

147

(19)

4 Linear Spaces

166

(36)

4.1 Introduction to Linear Spaces

166

(12)

4.2 Linear Transformations and Isomorphisms

178

(8)

4.3 The Matrix of a Linear Transformation

186

(16)

5 Orthogonality and Least Squares

202

(108)

5.1 Orthogonal Projections and Orthonormal Bases

202

(16)

5.2 Gram--Schmidt Process and QR Factorization

218

(7)

5.3 Orthogonal Transformations and Orthogonal Matrices

225

(11)

5.4 Least Squares and Data Fitting

236

(13)

5.5 Inner Product Spaces

249

(16)

6 Determinants

265

(1)

6.1 Introduction to Determinants

265

(12)

6.2 Properties of the Determinant

277

(17)

6.3 Geometrical Interpretations of the Determinant; Cramer's Rule

294

(16)

7 Eigenvalues and Eigenvectors

310

(75)

7.1 Diagonalization

310

(17)

7.2 Finding the Eigenvalues of a Matrix

327

(12)

7.3 Finding the Eigenvectors of a Matrix

339

(8)

7.4 More on Dynamical Systems

347

(13)

7.5 Complex Eigenvalues

360

(15)

7.6 Stability

375

(10)

 

Exams: There will be homework assignments after each class, three one-hour exams and a cumulative final exam:

Exam I  : Thursday, February 24

Exam II : Thursday, March 31

Exam III: Thursday, April 28

Final       : TBA

Grading Procedures: Exam 1: 20%, Exam 2: 25%, Exam 3: 25% Final exam: 30%.

THERE WILL BE NO MAKEUP EXAMS.

STUDENTS ARE RESPONSIBLE FOR MATERIAL COVERED IN CLASS.