Math 2130

Syllabus MATH 2130 / Fall 2020

This is an attempt. Things may change as we go.


Aug. 24First definitions: linear systems, solutions, classification of linear systems;
Solving linear systems: the basic rules, equivalent linear systems
Aug. 26Matrix encoding: LS as a matrix, echelon form of matrices, row reduction to echelon form.
Aug. 28The row reduction algorithm
Aug 31Vector equations


Sep. 02The matrix equation Ax=b
Sep. 04Solution sets
Sep. 07Labor day (no class)
Sep. 09Linear independence – I
Sep. 11Linear independence – II
Sep. 14Introduction to linear transformations
Sep. 16The (standard) matrix of a linear transformation; or the matrix of a linear transformation according to the canonical basis
Sep. 18Matrix operations
Sep. 21The inverse of a matrix
Sep. 23Subspaces of \mathbb{R}^n – I
Sep. 25Subspaces of \mathbb{R}^n – II
Sep. 28Midterm I review
Sep. 30Midterm I


Oct. 02Dimension and Rank
Oct. 05 Introduction to Determinants
Oct. 07Properties of Determinants
Oct. 09Cramer’s Rule, Volume and Linear Transformations
Oct. 12Vector Spaces and Subspaces
Oct. 14Null Spaces, Column Spaces – I
Oct. 16Null Spaces, Column Spaces – II
Oct. 19Linearly Independent sets; Bases – I
Oct. 21Linearly Independent sets; Bases – I
Oct. 23Coordinate Systems
Oct. 26Coordinate Systems
Oct. 28The Dimension of a vector space
Oct. 30Rank


Nov. 02Change of Basis – I
Nov. 04Change of Basis – II
Nov. 06Eigenvectors and Eigenvalues
Nov. 09The Characteristic equation
Nov. 11Midterm II Review
Nov. 13Midterm II
Nov. 16Diagonalization
Nov. 18Eigenvectors and Linear Transformations – I
Nov. 20Eigenvectors and Linear Transformations – II
Nov. 23Inner Product, Length and Orthogonality
Nov. 25Orthogonal sets
Nov. 27Thanksgiving (no class)
Nov. 30Orthogonal Projections


Dec. 02The Gram-Schmidt Process
Dec. 04Least-Square problems
Dec. 07Final Exam Review
Dec. 11Final Exam


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