Math 8: Transition to Higher Mathematics
Summer 2016
Syllabus
Instructor: Jared Kubler
Email: jwkubler@math.ucsb.edu
Lecture: MWF 11:0011:50 a.m. in Phelps Hall 3523
Office hours: MW 3:304:30 p.m. in South Hall 6431E
Teaching Assistant (TA): Abraham Schul
Math 8 Winter 2016: Homework 8
Due Fri, March 11, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom).
(1.) Let Cm be the congruence mod m relation defined in the text, for a positive integer m.
(a) Give a complete proof that Cm is an equiv
Math 8 Winter 2016: Homework 6
Due Wed, February 24, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom).
(1.) Suppose A, B, C, and D are sets.
(a) A x (B C) = (A x B) (A x C).
(b) (A x B) (C x D) = (A C) x (B D).
(2.) Suppose cfw_Ai | i I
Math 8 Winter 2016: Homework 5
Due Wed, February 17, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom).
(1.) Prove that there is a unique real number x such that for every real number y, xy+x4 =
4y.
(2.) (a) Prove that for all a, b R, |a|
Math 8 Winter 2016: Homework 4
Due Wed, February 3, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom),
but this material will be on the exam, so it is HIGHLY recommended that you complete
this assignment before the exam.
(0.) Again, it is
Math 8 Winter 2016: Homework 2
Due Wed, Jan 20, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom)
(1.) What are the truth sets of the following statements? List a few elements of the truth
set if you can.
(a) x is a real number and x2 4x
Math 8 Winter 2016: Homework 1
Due Wed, Jan 13, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom)
(1.) Analyze the logical forms of the following statements.
(a) Either John and Bill are both telling the truth, or neither of them is.
(b)
Math 8 Winter 2016: Homework 7
Due Fri, March 4, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom).
(1.) For each of the following theorems from the book, write out the proof in your own
words and filling in the steps left out.
(a) Theore
Math 8 Winter 2016: Homework 3
Due Wed, Jan 27, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom)
(0.) It is recommended that you spend some time looking at examples in the book. Some
of the material covered in lecture is from Sections 3.
Math 8 Winter 2016: Homework 2
Due Wed, Jan 27, 2016, 5pm, in mailbox of professor (South Hall 6th floor mailroom)
(0.) It is recommended that you spend some time looking at examples in the book. Some
of the material covered in lecture is from Sections 3.
PSTAT 120A: HW3 - Solutions
Problem 1.
Urn I contains 25 white and 15 black balls. Urn II contains 15 white and 25 black balls. An urn is
selected at random and ve balls are drawn randomly from this urn without replacement. If exactly
ve of these balls ar
3.3 Proofs Involving Quantifiers
1. In exercise 6 of Section 2.2 you use logical equivalences to show that
x(P (x) Q(x) is equivalent to xP (x) xQ(x). Now use the
methods of this section to prove that if x(P (x) Q(x) is true,
then xP (x) xQ(x) is true. (N