Lecture 1
Monday, September 28, 2015
9:03 AM
Deductive Reasoning
P stands for premises & Q stands for conclusion in this case.
Example 1) It will either rain (P) or snow (Q) tomorrow. It's too warm for snow (Q). Therefore, it
will rain (P).
P or Q; not
1.
ATP
(adenosine triphosphate) main energy source that cells use for
most of their work. Releases small amounts of energy that can be
used by cells.
2.
cellular respiration
Process that releases energy by breaking down glucose and other
food molecules in
ECON 2 GDP
Gross Domestic Product (GDP) measures the total market
value of all final goods and services produced within a country in
one year.
1. Intermediate goods (goods that are input in the production of
other goods) are not included in GDP to avoid d
University of California, Santa Barbara
Department of Mathematics
MATH 8:
Transition to Higher Mathematics
Instructor: Karel Casteels
E-mail: casteels@math.ucsb.edu
Oce: South Hall 6516
Oce Hours: Mon 10-12:00, Wed 12-2:00 (or by appointment)
Session: Fal
Math 8 Homework #1
Due: Thursday, October 8th, by 1:45pm in class or
submitted online at GauchoSpace
Instructions: Be sure to thoroughly justify all answers. I strongly recom-
mend that you attempt all problems on your own before consulting a class—
4
Math 8 Winter Quarter 2016
Homework 2
Due: Wednesday 20 January
1. Let A be the set cfw_a, cfw_1, a, cfw_4, cfw_1, 4, 4. Which of the following statements are true and which
are false?
(a) a A.
(b)cfw_a A.
(c) cfw_1, a A.
(d) cfw_4, cfw_4 A
(e) cfw_1, 4 A
Math 8 Winter Quarter 2016
Homework 1
Due: Monday 11 January
1. Analyze the logical forms of the following statements:
(a) 0 2 4.
(b)4 is a common divisor of 8, 12 and 16.
(c) Either John and Mary are both working or neither of them is.
2. Let P stand for
Home Work for Math 7H, Problem Set 2
Xining Li
October 20, 2015
1
Getting the least square minimum is like to get the value of the following equation.
n
(yi axi b)2
min
(1)
i=1
Dene y =
1
n
n
yi . Let b = y ax +
b
i=1
yi = axi + y ax +
b
(2)
yi y = a(xi
Home Work for Math 7H, Problem Set 1
Xining Li
October 17, 2015
1(a)
Whats the area of the parallelogram with corners at (0, 0), (5, 3), (8, 5), (3, 2)?
Because the area that we are going to calculate is of a parallelogram as shown, we can use cross
produ
Math. 34A, FALL 2015, MWF 9-9:50, Chuck Akemann (2 pages)
Prof. Chuck Akemann, South Hall 6706
Office Hours MWF 10:30-11:30,
phone 805-518-9555
e-mail: akemann@math.ucsb.edu
We are paid to help you learn.
Your TA: (fill in yourself)
PLEASE use CLAS, our
o
SUMMARY OF CLASS 5,
LINEAR ALGEBRA
We have shown that not every square matrix A is an invertible matrix.
Now we explore how to determine if a matrix is invertible and if so, how to
compute its inverse. The concepts that we will introduce next will help wi
HOMEWORK 4,
LINEAR ALGEBRA
October 6, 2015.
Solve at least four of the following questions.
Exercise 1 Let A, B Mnn (F ). Assume that AB = 0. Can we deduce
that A = 0 or B = 0? Prove or give a counterexample.
Exercise 2 Let A, B, C Mnn (F ). Assume that A
SUMMARY OF CLASS 3,
LINEAR ALGEBRA
Matrix (row-column) multiplication
Let A Fmn and B Fnr . Then, AB Fmr given by
n
(AB)ij =
Aik Bkj .
k=1
Note that the matrix multiplication is not a binary operation in the set
of all matrices or in the set of all rectan
HOMEWORK 3,
LINEAR ALGEBRA
October 1, 2015.
Solve at least four of the following questions.
Exercise 1 Let , F and let A, B Mpq (F ), where F is a eld. Prove
two of the following four properties of the scalar multiplication:
1. (A) = ()A,
2. ( + )A = A +
LINEAR ALGEBRA
Matrix algebra
Matrices are mathematical objects that are key in studying Linear Algebra. Here we introduce the arithmetic of matrices.
A matrix is a rectangular array of numbers, symbols, or expressions,
arranged in rows and columns. The i
HOMEWORK 2,
LINEAR ALGEBRA
September 29, 2015.
Do not worry if you cannot solve all the problems. Solve at least 4 of
them. The goal is to think about interesting problems and have fun. If you
have any questions about the statement of the problems, please
LINEAR ALGEBRA
Algebraic structures with two operations.
Now we consider algebraic structures in which two binary operations are
dened.
Denition 1 Let S be a nonempty set in which two binary operations + and
have been dened. Then, (S, +, ) is said to be a