Discrete structures course information

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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

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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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