**Course Description:** AMS 10 provides an introduction to linear algebra and its applications. In addition, students will learn to use computational software (MATLAB/OCTAVE) and the basics of numerical linear algebra.

**Instructor: **Prof. Daniele Venturi (venturi@ucsc.edu)

Teaching Assistants: Lia Gianfortone (lgianfor@ucsc.edu), Yuanran Zhu (yzhu22@ucsc.edu), Long Lu (lklu@ucsc.edu)

Main Lectures: Tu/Th 3:20PM-4:55PM, Earth & Marine Sciences B206

Sections: Tu/Th 7:10PM-8:45PM BE-152 (**Webcast Link** **user:** am-10-1 **password:** AM10_section)

**CANVAS COURSE WEBPAGE: AM10**

Group tutoring sections: MWF 12PM-1PM, Social Sciences 1, room 153.

**Office Hours: **

- Prof. Venturi, Monday 10AM-12PM BE-361C
- Yuanran Zhu, Wedensday 4-6PM BE 153 A
- Lia Gianfortone, Tuesday 11AM-1PM BE-312
- Long Lu, Friday 10AM-12PM BE118

**Homework Assignments: **Homework assignments will not be collected or graded. The quiz problems and the final exam problems will be very similar to homework problems.

**Quizzes and Exams****: **There will be in-class quizzes, and a comprehensive final exam.

Quizzes (tenative dates): Oct. 15, Oct. 29, Nov 12, Nov 26.

Final Exam: Monday Dec 9th, 4-7PM Earth & Marine Sciences B206.

**Grading Policy: **70% in-class quizzes, 30% comprehensive final exam.

**Tentaive syllabus: **

*Week 1:*Real numbers and introduction to complex numbers*Week 2:*Complex numbers, algebraic and polar form, De Moivre formula, complex exponential function, nth root of a complex number, quadratic quations and polynomial equations in the complex plane.*Week 3:*Homogeneous linear equations, matrices, row operations and Gauss elimination, linear combination*Week 4:*Matrix algebra, multiplication and addition, matrices associated with linear systems, LU factorization acorresponding to Gauss elimination. Gauss elimination as*Week 5:*Vector spaces, linear combinations, convex sets, linear independendence, dimension, matrix rank*Week 6:*Linear Maps, kernel and image of a linear map, matrix associated with a linear map, change of bases*Week 7:*Scalar products, orthogonal bases, bilinear maps and matrices*Week 8:*Determinants, Cramer's rule, inverse of a matrix*Week 9:*Eigenvalues and eigenvectors, characteristic polynomial, geometric and algebraic multiplicity of eigenvalues.*Week 10: S*imilarity transformations, diagonalization

**Textbooks:**

- Serge Lang, ``Introduction to linear algebra'', Springer

https://link.springer.com/

- Serge Lang, ``Llinear algebra'', Springer

https://link.springer.com/book/10.1007/978-1-4757-1949-9 (free download from campus network)

- David Lay,
*``*Linear algebra and its applications''