Discrete Structures I
Dalhousie University
MATH/CSCI 2112
Winter 2017
• Instructor: Nauzer Kalyaniwalla, CS 221; 494-2841 [email protected]
• Times: MWF 11:35 - 12:25 LSC C242.
• Office Hours: Wed 1:30 - 3:00; Thu 10:30 - 12:30/Open door
• Web: hhtps://dal.brightspace.com
• Texts: (i) Book of Proof by Richard Hammack, available online at:
http://www.people.vcu.edu/∼rhammack/BookOfProof/
(ii) Lectures in Discrete Mathematics, by Edward A. Bender and S. Gill Williamson
(A source of practice problems), available on-line at:
http://cseweb.ucsd.edu/∼gill/BWLectSite/
A schedule of topics and class notes will be posted on the course page on Brightspace.
Students are responsible for material covered in class.
• Evaluation:
Assignments 25 % ∼8 in total
Test I
20 % 6 Feb (in class)
Test II
25 % 7 Mar (6:00-7:30pm)
Test III
30 % Sched. by Registrar
Conversion of numerical grades to final letter grades follows the Dalhousie Common Grade
Scale
• Course Description: Discrete math provides the tools for the mathematical foundations
of computer science as well as advanced mathematics courses. The goal of this course is
to build basic skills in mathematical reasoning. This includes a familiarity with: Logic
and sets; counting techniques; some number theory, especially modular arithmetic; proof
techniques (direct, by cases, by contradiction, by contrapositive and by induction); recursive
functions and algorithms; cardinality of sets.The first few weeks of the course introduces
the critically important logical framework and mathematical language used throughout the
course.
• Calendar Description: This course together with MATH/CSCI 2113.03 offers a survey of the following areas: set theory, mathematical induction, number theory, relations,
functions, algebraic structures and introductory graph theory. The topics to be discussed
are fundamental to most areas of Mathematics and have wide applicability to Computer
Science. This course requires NS Math 441/equivalent as a prerequisite.
• Intellectual Honesty: It is expected that students will discuss assignment problems and
help each other but students are expected to hand in only their own effort. All assigned
problems are expected to be “done from scratch” (It will pay to attempt them on your
own). Avoid searching for solutions on the Internet etc. Document any help received and
any resources used.
To this end please look at the information and resources available at:
http://academicintegrity.dal.ca and
the full text of Dalhousie?s Policy on Intellectual Honesty and Faculty Discipline Procedures at:
www.dal.ca/dept/university secretariat/academic-integrity/academic-policies.html .
In addition, Dalhousie University’s student code of conduct can be found at:
http://www.dal.ca/dept/university secretariat/policies/student-life/code-of-student-conduct.html
Please refer to the course web-page for further resources available to you.
1
Week of Topics
9 Jan Introduction; Logic and Boolean functions
In Text
BoP 1.2; 2.1-2.5 (units BF, Lo-1)
16 Jan Predicate Logic, Inference
BoP 2.7 - 2.12 + notes (unit Lo-2)
23 Jan Counting
BoP 1.3, 1.4; Ch 3; 12.3
30 Jan Counting (continued)
BoP 1.3, 1.4; Ch 3; 12.3
3 Feb MUNRO DAY
no class.
6 Feb TEST I
in class
8 Feb Proofs and Number Theory
BoP 4, 5, 6, 7 (unit NT)
13 Feb Proofs and Number Theory continued
20 Feb WINTER BREAK
no classes
27 Feb Introduction to Induction
BoP 1.9; Ch.10, (unit IS) + notes
6 Mar Induction continued . . .
7 Mar TEST II
Tue 6:00pm - 8:00pm Loc:TBA
13 Mar Recursively defined functions and algorithms. BoP 10 + notes
21 Nov Recursively defined functions and algorithms
(contd.).
28 Mar Eq. Relations and Linear Congruences; FLT
3 Apr Cardinality of Sets;
BoP 1.2; 11; + notes
BoP 1.10; 13 + notes
10 April Review
Table 1. BoP: Book Of Proof; units BF, Lo, NT, IS: Lectures in Discrete Math
• Weekly Schedule, (subject to change) updated regularly on Brightspace: