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Students are presumed to be familiar with basic programming techniques, including the use of functions and procedures, loops and recursion. Also assumed is facility with basic algebra.

Students are also expected to be familiar with the use of standard Internet-based tools including e-mail.

Course objectives

  • Cultivate clear thinking and creative problem solving.
  • Thoroughly train in the construction and understanding of mathematical proofs. Exercise common mathematical arguments and proof strategies.
  • Cultivate a sense of familiarity and ease in working with mathematical notation and common concepts in discrete mathematics.
  • Teach the basic results in Mathematical Logic, Set Theory, and Relations.

Student objectives

At the end of the course, students should:

  • Understand fundamental mathematical concepts as they apply to computer science by seeing how mathematics supports CS, and how CS concepts can be formalized in mathematics
  • Illustrate by examples the basic terminology of functions, relations, and sets and demonstrate knowledge of their associated operations.
  • Establish and solve recurrence relations that arise in counting problems including the problem of determining the time complexity of recursively defined algorithms.
  • Model logic statements arising in algorithm correctness and real-life situations and manipulate them using the formal methods of propositional and predicate logic.
  • Outline basic proofs for theorems using the techniques of: direct proofs, proof by counterexample, proof by contraposition, proof by contradiction, and mathematical induction.
  • Relate the ideas of mathematical induction to recursion and recursively defined structures.
  • Enhance one’s ability to program by seeing how mathematical concepts form the basis for many common programming problems (e.g. grammars for parsing, predicate calculus for logic programming, sets and algebras for relational databases, graphs and topological sorting for automating optimization).
  • Further their ability to write large programs by integrating code from a diverse spectrum of program components.

Grading procedures

The overall grade for this course is based on your performance in (i) exercises, (ii) assignments, (iii) mid-term exam and (iv) final exam, with weights as given below. Exams consist of a midterm and a final exam.

Course component grading weight (it can be changed):

  • Midterm: 20%
  • Weekly homework: 40%
  • Final: 40%

Content information

First we learn a general methodology for solving problems. This methodology is going to be followed in solving problems, and in proving theorems throughout this course.

The next subject is logic. Logic subject matter is covered in Chapter 1 of the textbook. “Logic” is a language that captures the essence of our reasoning, and correct reasoning must follow the rules of this language. We start with logic of sentences called propositional logic, and study elements of logic, (logical) relationships between propositions, and reasoning. Then we learn a little more powerful logic called predicate logic. Predicate logic allows us to reason with statements involving variables among other statements.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Discrete structures. OpenStax CNX. Jan 23, 2008 Download for free at http://cnx.org/content/col10513/1.1
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