Math/CS 103
Professor: Padraic Bartlett
Homework 9: The Geometry of Linear Maps
Due 10/25/13, at the start of class.
UCSB 2013
This problem set contains ve questions. Choose three of the ve problems below to
complete by next class. Be ready and able to pr

Math/CS 103
Professor: Padraic Bartlett
Homework 8: Color Space
Due 10/21/13, at the start of class
UCSB 2013
Hi! A brief physics and biology lesson.
Light! It exists. In particular, a given photon of light has some set wavelength,
measured in this probl

Math/CS 103
Professor: Padraic Bartlett
Homework + Lecture 7: Linear Map Properties
Due 10/18/13, at the start of class
UCSB 2013
More denitions! In theory, we talked about all of these at the end of class on Monday.
1
Background.
Denition. Let V be a vec

Math/CS 103
Professor: Padraic Bartlett
Homework 6: Linear Maps
Due 10/14/13, at the start of class
UCSB 2013
This sets a little dierent. First, recall from class that weve introduced two examples
of nite-dimensional vector spaces:
Rn , the collection of

Math/CS 103
Professor: Padraic Bartlett
Homework 5: The Signal and the Noise
Due 10/11/13, at the start of class
UCSB 2013
Choose three of the six problems below to complete by next class. Be ready and able to
present your solutions if you have them, or y

Math/CS 103
Professor: Padraic Bartlett
Homework 4: Calculators!
Due 10/7/13, at the start of class
UCSB 2013
Choose three of the ve problems below to complete by next class. Be ready and able
to present your solutions if you have them, or your questions

Math/CS 103
Professor: Padraic Bartlett
Homework 3: Exploring the Seas
Due 10/4/13, at the start of class
UCSB 2013
Choose three of the ve problems below to complete by next class. Be ready and able
to present your solutions if you have them, or your ques

Math/CS 103
Professor: Padraic Bartlett
Homework 2: Submarines and Sabotage
Due 10/2/13, at the start of class
UCSB 2013
Choose three of the ve problems below to complete by next class. Be ready and able
to present your solutions if you have them, or your

Math/CS 103
Professor: Padraic Bartlett
Homework 10: Injection, Bijection, Surjection
Due 10/28/13, at the start of class.
UCSB 2013
To do this problem set, you need the following denitions:
Denition. A function f with domain A and codomain B , formally s

Math/CS 103
Professor: Padraic Bartlett
Homework 11: More Injections, Surjections and Linear Maps
Due 11/1/13, at the start of class.
UCSB 2013
This problem set contains eight questions. Choose three of the eight problems below
to complete by next class.

Math/CS 103
Professor: Padraic Bartlett
Lecture 1: The Art and Technique of Argument
Week 0
1
UCSB 2013
What is a Proof ?
Every major eld of study in academia, roughly speaking, has a way of showing that
something is true. In English/critical literature s

Math/CS 103
Professor: Padraic Bartlett
Lecture 10: Injection, Surjection, and Linear Maps
Week 5
UCSB 2013
This talk is designed to go over some of the concepts weve been exploring recently with
injections, surjections, and linear maps.
1
Injection, Surj

Math/CS 103
Professor: Padraic Bartlett
Lecture 9: Understanding Null Space
Week 4
UCSB 2013
In our last full lecture, we introduced the concept of null space. In todays talk, we
return to this object, with a new focus on why we care about the concept of

Math/CS 103
Professor: Padraic Bartlett
Lecture 8: Linear Transformations
Week 3
UCSB 2013
Todays lecture is on the concept of linear maps, which weve been studying in the
past few problem sets. We start by reviewing the content from problem sets 6 and 7,

Math/CS 103
Professor: Padraic Bartlett
Lecture 5: Dot Products
Week 2
UCSB 2013
Hello! This mini-lecture is designed to introduce the dot product. We do this below:
1
Dot Products
Homework 5 is basically centered around the dot product operation, dened h

Math/CS 103
Professor: Padraic Bartlett
Lecture 5: Polynomials and Vector Spaces
Week 2
UCSB 2013
Hello! This mini-lecture is designed to introduce the concept of polynomials in the
language of vector spaces. We do this below:
1
Polynomials and Vectors
Mo

Math/CS 103
Professor: Padraic Bartlett
Lecture 4: Basis and Dimension
Week 1
UCSB 2013
Hello! This mini-lecture is designed to introduce the concepts of basis and dimension.
We do this below:
1
Basis and Dimension
On your third problem set, you dealt wit

Math/CS 103
Professor: Padraic Bartlett
Lecture 3: Linear Dependence and Independence
Week 1
UCSB 2013
Hello! This mini-lecture is designed to introduce the concepts of linear independence
and dependence. We do this below:
1
Linear Independence and Depend

Math/CS 103
Professor: Padraic Bartlett
Lecture 2: Vector Spaces
Week 1
UCSB 2013
Hello! This mini-lecture is designed to introduce the concepts of vector spaces and
span, a pair of concepts we studied on the past homework.
1
Vector Spaces: Examples
As of

Math/CS 103
Professor: Padraic Bartlett
Homework 1: Seas and Space
Due 9/30/13, at the start of class
UCSB 2013
Choose three of the ve problems below to complete by next class. Be ready and able
to present your solutions if you have them, or your question