Math 115A is a core mathematics course required of all the various mathematics majors. The course material can be regarded as an elaboration of the linear algebra already covered in Math 33A. However, the level of abstraction and the emphasis on proof technique make this a difficult course for many students. Successful students emerge from the experience not only with a better understanding of linear algebra, but also with a higher level of mathematical maturity, better equipped to deal with abstract concepts.
Instructor
Omprokash Das
Teaching Assistant
Young Hak Kwon
Lecture Time / Location
MWTh, 11am-12:50pm @ MS 6627
Discussion Time / Location
Tu, 11am-12:50pm @ MS 6627
# | Date | Description |
---|---|---|
1.2 | ^{6}/_{25} | Vector Spaces Spaces, Vector Spaces, Degree of Polynomial, Fields. [Notes] |
D.1 | ^{6}/_{25} | Discussion [Notes] |
1.3 | ^{6}/_{27} | Subspaces Subspaces. [Notes] |
1.4 | ^{7}/_{2} | Linear Combinations and Systems of Linear Equations Linear Combination, Span, Generating Set. [Notes] |
1.5 | ^{7}/_{3} | Linear Dependence and Linear Independence Linearly Dependent, Linearly Independent. [Notes] |
D.2 | ^{7}/_{3} | Discussion [Notes] |
1.6 | ^{7}/_{5} | Bases and Dimensions Basis, Dimensions of Vector Spaces. [Notes] |
D.3 | ^{7}/_{10} | Discussion [Notes] |
2.1 | ^{7}/_{11} | Linear Transformation Linear Transformation, Identity Transformation, Zero Transformation, Kernel (Null Space), Range (Image), Nullity, Rank, One-to-One, Onto. [Notes] |
2.2 | ^{7}/_{16} | The Matrix Representation of a Linear Transformation [Notes] |
D.4 | ^{7}/_{17} | Discussion [Notes] |
2.3 | ^{7}/_{18} | Composition of Linear Transformations and Matrix Multiplication [Notes] |
2.4 | ^{7}/_{19} | Invertibility and Isomorphisms [Notes] |
2.5 | ^{7}/_{23} | The Change of Coordinate Matrix [Notes] |
D.5 | ^{7}/_{24} | Discussion [Notes] |
5.1 | ^{7}/_{25} | Eigenvalues and Eigenvectors [Notes] |
5.2 | ^{7}/_{26} | Diagonalizability [Notes] |
6.1 | ^{7}/_{30} | Inner Products and Norms [Notes] |
D.6 | ^{7}/_{31} | Discussion [Notes] |
6.2 | ^{7}/_{31} | Gram-Schmidt Orthogonalization Process [Notes] |
Resources
- [1]Terence Tao. Lecture Note, sample exams, and solutions. UCLA MATH 115A - Fall 2002 course site. URL: http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/
- [2]Michael Andrews. Outline of lectures, and homework. UCLA MATH 115A - Winter 2018 course site. URL: http://www.math.ucla.edu/~mjandr/Math115A/index.html