**Prerequisite:**MATH 1553 or MATH 1554 or MATH 1564 or MATH 1502 or MATH 1512 or MATH 1522 or MATH 1X53.

**Meeting time**: TuTh 1:30-2:45 in Skiles 270

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**Office hours:**M10:30-12, W1-2:30, or by appointment. All students are required to attend an OH before the midterm.

**Required Text:**Linear Algebra with Applications, 4th North American ed, Gilbert Strang (I plan to cover chapters 1-6, A1, and A2)

**Grading:**Bi-weekly problem sets (20%), 2 exams (40%), final exam (40%). The final exam grade may replace an exam grade.

Final grades will be calculated as follows: A:90-100, B:80-89, C:70-79, D:60-69, F: <60. Class participation will determine borderline grades.

Official Syllabus

**Linear algebra**is the branch of mathematics which studies vector spaces and

**linear**mappings between them. Linearity places very strong constraints on a mapping. For instance, if f: R^n->R^n is linear, then f is completely determined by evaluating it on n points. This second course will further your understanding of the ideas and methods of linear algebra in abstract vector spaces. You will learn by understanding them geometrically, justifying them algebraically, and using them to solve problems in various disciplines. You willl be required to understand all key concepts as well as compute with them.

Although we live in a nonlinear world, linear algebra remains an essential subject with applications throughout mathematics and its applications. There are several reasons for this, including, that in a large number of cases, useful insights about non-linear transformations can be obtained from their linear approximations. You have seen this line of thinking in calculus, where arbitrary smooth functions are studied via their derivatives - their best linear approximations. Luckily, as you will see during the course, we have a useful and beautiful theory which provides many tools to solve linear problems. The course is centered around solving four equations: Ax=b, A'Ax=A'b, Ax=λx, and du/dt=Au.

Gilbert Strang argues that applications of linear algebra touch many more students than calculus. These days, much of "big data" arrives in matrix form and machine learning tools utilize linear algebra. Applications in this course will depend somewhat on student interests, but last semester included principal component analysis, image compression, graph theory, Markov chains, Google's PageRank, solving linear ODEs and difference equations, fast Fourier transform, and demography.

**Learning Objectives**

- How to analyze and solve a linear system of equations, and if it can’t be solved, find the best approximate solution (least squares and pseudo-inverses)
- Important characteristics of matrices, such as their four fundamental subspaces, rank, determinant, eigenvalues and eigenvectors
- How to factorize matrices in useful ways, such as A=LU, A=QR, diagonalization, Jordan form, triangular form, singular value decomposition, and polar decomposition
- Important concepts of vector spaces such as independence, basis, dimensions, orthogonality, etc. as well as sums, products, and tensor products of vector spaces
- Properties of special matrices, such as symmetric, triangular, positive definite, Hermitian, unitary, nilpotent, and normal matrices
- Introduction to Matlab for linear algebra
- Applications of linear algebra in the sciences and engineering
- Practice clear, concise communication of mathematical ideas