Math 61
Tufts University Dept of Mathematics
Final Exam Review Material
Exam date: Dec 13 2012
Prof. McNinch
The nal exam covers the material we covered from the following sections in the text:
9.1, 9.2, 9.3, 9.4, 9.5 (Relations)
10.1, 10.2 (Graphs)
1.
Math 061-01
1.
Tufts University Dept of Mathematics
Final Exam
Dec 13, 2012
Prof. McNinch
(15 points) Give careful denitions of the following terms:
(a) a relation from a set X to a set Y .
(b) the transitive closure of a relation R on a set X .
(c) an un
Tufts University
Department of Mathematics
Exam 2 Review Sheet
Discrete Math
Fall 2013
PART IV: PROBABILITY
1. Let A and B be events in a sample space S, and suppose A B = , P (A) = 0, and P (B ) = 0. Show
that P (A B ) = P (A) P (B ).
2. Suppose A and B
Tufts University
Department of Mathematics
Exam 1 Review Sheet
Discrete Math
Fall 2013
PART I: COMBINATORICS
1. What is the statement of the (a) binomial theorem? (b) the multinomial theorem?
2. How many ways are there to place 25 dierent ags on 10 number
MATH/COMP61-03 Spring 2014:
Homework 1
This homework is due Tuesday, January 28th at the beginning of class. If you
have substantially collaborated with other students on a problem, please acknowledge
this at the top of your homework sheet. No credit will
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Spring 2013
HW 12: due Monday, April 29
Your third in class exam is on the last day of class: Monday, April 29th. It will
cover material in HWs 10, 11, and 12, i.e. graphs, divisibi
MATH/COMP 61-02: Discrete Mathematics
Tufts University
HW 11: due Wed, April 24 in class
From Rosen do problems:
Section 4.1 (pp. 244-245): 34, 35, 36, 37, 38
Section 4.3 (pp. 272-274): 21, 22, 23, 32ce, 34
Prof. Lenore Cowen
Spring 2013
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Spring 2013
HW 10: due Wed, April 17 in class
Remember, no class on Mon, April 15 (Tufts holiday)!
From Rosen do problems:
Section 10.3 (pp. 675-678): 44, 50, 51, 52, 53, 54c, 55, 5
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 1: due Tues, Sept 10
Part I: From Raymond Smullyans What is the Name of this Book?:
When Alice entered the Forest of Forgetfulness, she did not forget everything, only
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 3: due Tuesday, September 24
Part I:
A. Does the conclusion follow? Justify your answer by writing the argument down
formally and using the rules of inference. I am a f
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 4: due Tues, October 1
Your rst exam will be Thurs, October 3 in class. It will cover the material on hws
1-4, i.e. chapter 1, sections 2.1 and 2.2 and 5.1 and 5.2 in y
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 5: due Thursday, October 17
Please note that there is NO CLASS on Tuesday, October 15 because Tufts is on a
Monday schedule!
From Rosen do problems:
Section 6.1 (pp.395
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 7: due Thursday, Oct 31
Note: This hw is not hard, but its long. Start early!
From Rosen do problems:
Section 9.1 (pp. 581-583): 3ade, 4bd, 6abeg, 8, 36abcd, 40ab, 42,
MATH/COMP 61-02: Discrete Mathematics
Tufts University
Prof. Lenore Cowen
Fall 2013
HW 8: due Thurs, Nov 7 in class
Your second in class exam will be on Thursday, Nov 14 in class. It will cover
counting, functions, relations and the beginning of graphs (i