EE103: Course Information

Lectures

Tuesdays and Thursdays, 9am–10:20am, Bishop Auditorium.

Sections

The sections will meet weekly starting the week of October 3. The sections will be 2 hours long, with the first hour or so spent on covering applications, and the remaining time used as office hours.

  • Mark Nishimura: Tuesday, 2:30-4:30pm at Littlefield Center 103 (L103)

  • Enzo Busseti: Tuesday, 3:30-5:30pm at 260-004

  • Vikram Prasad: Tuesday, 4:30-6:30pm at GESB 134

  • Guillermo Angeris: Tuesday, 6:00-8:00pm at 260-004

  • Reese Pathak: Tuesday, 7:00-9:00pm at 260-003

  • Extra Section (staffed on a rotating basis): Wednesday, 10:30am-12:30pm at 420-050

  • Pin Pin Tea-Mangkornpan: Wednesday, 1:30-3:30pm at ART 360

  • Do-Hyoung Park: Wednesday, 3:30-5:30pm at 380-381T

  • Richard Mu: Wednesday, 6:00-8:00pm at 380-381U

  • Jihee Hwang: Wednesday, 7:00-9:00pm at 260-004

  • Karen Leung: Thursday, 1:30-3:30pm at 260-004

  • Lin Fan: Thursday, 3:00-5:00pm at 200-303

Office hours

Stephen Boyd's office hours: Tuesdays 10:20am–12pm, and Wednesdays 1:30pm–3pm, Packard 254.

TA office hours: The TAs’ office hours will be folded into the last hour (or so) of the weekly sections.

Additional office hours: Additional office hours will be held Thursdays 3:30pm–5:30pm in Huang basement. These office hours will be staffed by 1-2 TAs each week.

Textbook

The textbook is a draft that is being written by Stephen Boyd and Lieven Vandenberghe, which will be posted on-line, and updated every so often as they edit it. You will not need to consult any other books or materials (though you are welcome to do so).

Course requirements and grading

Requirements:

  • Attendance at lectures.

  • Attendance and participation at sections.

  • Weekly homework assignments. Homework will normally be assigned each Friday, and due the following Friday by 5pm in the box accross from Packard 243. Late homework will not be accepted.

  • Midterm exam. The miderm will be in class, Thursday October 27, 9am–10:20am.

  • Final exam. The final exam is scheduled for Wednesday December 14, 8:30am–11:30am.

Grading: Attendance/participation 5%, homework 30%, midterm exam 25%, final exam 40%.

Prerequisites

You do not need to have seen any linear algebra before; we will develop it from scratch. Math 51 is nominally a prerequisite, but we will use very little of this material. In the course you'll do some very simple programming in the language Julia, so you should have seen some very basic simple programming. CS106A or equivalent (which is more than you will need) is a prerequisite or corequisite. You do not need to know about any applications; we'll cover that in detail. Even if you have already seen all the material in the course (e.g., vectors, matrices, least-squares) we encourage you to take it, because (we guess) you haven't seen it the way we will present it.

Syllabus

Vectors

Topics: Vectors, inner product, norm, distance, RMS value, angle, mean, standard deviation; k-means algorithm.

Applications: Audio mixing, monochrome and color images, time series, feature vectors, document analysis via word counts, asset returns.

Linear independence

Topics: Dependent and independent sets of vectors, basis, orthonormal sets of vectors, independence-dimension inequality, Gram-Schmidt algorithm.

Matrices

Topics: Matrices, transpose, matrix-vector multiplication, linear and affine functions, systems of linear equations.

Applications: Word count matrices, feature matrices, polynomial interpolation, stoichiometry, linear dynamical systems (population dynamics, ballistics), image blurring, tomography.

Matrix multiplication

Topics: Matrix-matrix multiplication, composition of linear and affine functions, matrix powers, QR factorization.

Applications: Linear dynamical systems, counting paths in graphs.

Matrix inverses

Topics: Left and right matrix inverses, matrix inverse, solving linear equations via QR factorization, pseudo-inverse.

Applications: Polynomial and rational interpolation, ballistics targeting, balancing chemical equations.

Least-squares

Topics: Basics ideas of least-squares methods, solving least-squares problems using QR factorization, data-fitting, validation.

Applications: Fitting 1-D data with a constant, affine function, or polynomial. Regression, auto-regressive time series models, robust ballistics targeting, least-squares classification.

Multi-objective least-squares

Topics: Multi-objective least-squares via weighted sums, regularization.

Applications: Image deblurring, tomography, handwritten digit classification, time series analysis and prediction, image in-painting.

Equality constrained least-squares

Topics: Equality constrained least-squares, least-norm problem, solution methods.

Applications: Portfolio optimization, control, dynamic system estimation.

Catalog description

Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series prediction, tomography, optimal control, and portfolio optimization. Prerequisites: MATH 51 or CME 100, and basic knowledge of computing (CS 106A is more than enough, and can be taken concurrently).

EE103 is part of the EE and MS&E core requirements, approved for the CS BS Math Elective and the Mathematics & Statistics requirement in the School of Engineering, and certified as a Ways of Thinking (Formal Reasoning) course.

EE103/CME103 and Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of Math 104 is on algorithms and concepts.

Course objectives

The goal of this course is to introduce you to the basic ideas of vectors, matrices, and (very basic) linear algebra, emphasizing applications. We hope that you'll learn how linear algebra is all around you, and how it is used in zillions of applications. You'll learn some basic machine learning, portfolio optimization and finance, audio and image processing, and other applications.

Intended audience

The course will ultimately be targeted at undergraduate students in all fields, just as CS106a is. But for now (until we shake the course out) we are targeting students with a little more background in math, CS, and related areas.