**Instructor:** Shiang Tang

**Course on canvas.dartmouth.edu.**⇗

## Course Description

Linear algebra is the study of vector spaces and the linear transformations between such spaces. In this class we will work mostly with the vector space Rn. We will learn how to represent linear transformations with matrices and study different types of linear transformations, such as diagonalizable transformations. During the last week of classes we will concentrate on applications. For a more detailed description on the topics we will learn in this class see Pages.

Linear algebra is very important for both pure and applied mathematics. This is one of the reasons that it is a prerequisite for almost all of your math major courses and other STEM subjects. The techniques of linear algebra are used in engineering, physics, natural sciences, computer science and economics. For example, when we combine calculus with linear algebra we can solve linear systems of differential equations.

Goals of the course:

- Students will learn the main concepts and techniques in linear algebra.
- Students will learn some applications of linear algebra.
- Students will be prepared for more advanced courses in mathematics, computer science, physics and any other subjects that require linear algebra.

## Textbook

David Lay, Lay and McDonald Linear Algebra and its applications, Fifth edition (ISBN: 978-0321982384).

## Tentative schedule

**Week 0**

<Thu, 6/20> 1.1-1.2: systems of linear equations, row reductions and echelon forms

**Week 1**

<Tue, 6/25> 1.3-1.4: vector equations, matrix equations

<Thu, 6/27> 1.5, 1.7: solution sets of linear equations, linear independence

WW1-2 due on Tue, WW3 due on Thu, HW1 due on Thu

**Week 2**

<Tue, 7/2> 1.7, 4.1-4.2: vector spaces, null space and column space, linear transformations

<Thu, 7/4> NO CLASS

WW4-5 due on Tue

**Week 3**

<Tue, 7/9> 4.2, 1.9: kernel and range, matrix of a linear transformation, 1-1 and onto

<Thu, 7/11> 2.1-2.2: matrix operations, invertibility of a matrix

WW6-7 + HW2 due on Tue, WW8 due on Thu

**Week 4**

<Tue, 7/16> 2.3, 4.3: invertible matrix theorem, linearly independent sets

**Exam 1 on Wed, 7/17, 6:30-8:30 pm in Kem 007 (materials up to 7/11)**

<Thu, 7/18> 4.3, 2.9: bases, coordinates, dimension and rank

WW9 + HW3 due on Tue, WW10 due on Thu

**Week 5**

<Tue, 7/23> 4.4, 5.4, 4.7: matrix of a linear transformation, change of coordinate matrix and composition of linear transformations

<Thu, 7/25> 3.1-3.2: determinants and their properties

WW11 + HW4 due on Tue, WW12-14 due on Thu

**Week 6**

<Tue, 7/30> 5.1-5.2: eigenvalues and the characteristic equation

<Thu, 8/1> 5.3-5.4: diagonalization, diagonalization and linear transformations

WW15 + HW5 due on Tue, WW16-17 due on Thu

**Week 7**

<Tue, 8/6> 6.1-6.3: inner product and orthogonality, projections

**Exam 2 on Wed, 8/7, 6:30-8:30 pm in Kem 007**

<Thu, 8/8> 6.3-6.4: projections, Gram-Schmidt process

WW18 + HW6 due on Tue, WW19 due on Thu

**Week 8**

<Tue, 8/13> 7.1, 4.9: diagonalization of symmetric matrices, intro to Markov chains

<Thu, 8/15> 4.9, 5.8: iteration method for eigenvalues, Markov chains and Google's page rank

WW20-21 + HW7 due on Tue

**Week 9**

<Tue, 8/20> review for the final

WW22 + HW8 due on Tue

**Final Exam: Mon, 8/26, 3-6 pm in Kem 007**