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