Foundation of Logical Thoughts(FOLT)
Course Overview and Motivation
Instructor: Dr. Dinesh Kumar
CS-13104: Foundations of Logical Thoughts
(Credits: 4-0-0-4)
Instructor: Dr. Dinesh Kumar
Email for Official Communication:
dinesh.kumar@mnnit.ac.in
Contact Number: +91-7015595587
Course Outline (to be covered in 40 lectures)
• Unit 1: Introduction, Set theory, Notion of proofs , Linear
congruence (8)
• Unit 2: Formal logic: Propositional Logic, Relational logic,
First order logic, and related issues (8)
• Unit 3: Lattices and related issues (8)
• Unit 4: Group Theory and related issues (6)
• Unit 5: Finite Fields and related issues (6)
• Unit 6: Generating Functions and related issues (4)
Textbooks
• Manohar: Discrete Mathematical Structure with Application to
Computer Science”, J.P
Trembley, & R. Manohar.
https://www.amazon.in/DISCRETE-MATHEMATICAL-STRUCTURES-
APPLICATIONS-COMPUTER/dp/0074631136
• Schaum’s DM: Lipschutz S. Schaum's Outlines of Theory and Problems
of Discrete Mathematics., 2016.
https://www.amazon.in/Schaums-Outline-Discrete-Mathematics-
S/dp/0070380457
Textbooks …
• Schaum’s Abstract Algebra: Jaisingh LR, Ayres F. Schaum's Outline of Abstract
Algebra. McGraw Hill Professional; 2003
https://www.amazon.in/Schaums-Outline-Abstract-Algebra-
Outlines/dp/0071403272
• Rosen: Discrete Mathematics and Its Applications Seventh Edition 7th Edition by
Kenneth Rosen, McGraw Hill.
https://www.amazon.in/Discrete-Mathematics-Applications-Kenneth-
Rosen/dp/0073383090/ref=sr_1_2?dchild=1&keywords=Discrete+Mathematics+an
d+Its+Applications+Seventh+Edition&qid=1596876353&s=books&sr=1-2
• The Indian version of the above book is:
• https://www.amazon.in/Discrete-Mathematics-Its-Applications-
SIE/dp/0070681880/ref=sr_1_1?dchild=1&keywords=Discrete+Mathematics+and
+Its+Applications+Seventh+Edition&qid=1596876353&s=books&sr=1-1
Unit 1: Introduction, Set theory, Notion of
proofs , Linear congruence
Set Theory Manohar(Ch. 2.1)
Relations Manohar(Ch. 2.2 )
Functions and Recursion Manohar (Ch. 2.4, 2.6)
Number Theory Rosen (Ch. 4)
Schaum’s DM (Ch. 11)
Schaum’s Abstract Algebra
(Ch. 5)
Unit 2: Formal logic: Propositional Logic, Relational
logic, First order logic, and related issues
Logic Manohar(Ch. 1)
Rosen (Ch. 1)
Unit 3: Lattice and Related Issues
Lattice Manohar (Ch. 4)
Boolean Algebra Schaum’s DM (Ch. 14,15)
Schaum’s Abstract Algebra
(Ch. 18)
Rosen (Ch. 12)
Unit 4: Group Theory and Related Issues
Abstract Algebra Manohar (Ch. 3)
Schaum’s DM (Appendix B)
Schaum’s Abstract Algebra
(Ch. 9,10)
Unit 5: Finite Field and Related Issues
Rings Schaum’s Abstract Algebra
Integral domain, division (Ch. 11,12)
Rings and Fields
Unit 6: Generating Functions and Related
Issues
Recurrence Relation and Rosen (Ch. 8)
Generating Function
Why we are studying this Course?
• Mathematical Reasoning (Formal Logic)
• Students must understand mathematical reasoning in order to
read, comprehend, and construct mathematical arguments.
• Combinatorial Analysis (Generating Functions and Recurrence
Relation)
• An important problem-solving skill is the ability to count or enumerate
objects
Why we are studying this Course?
• Discrete Structures (Set Theory, Relation and Functions)
• course in discrete mathematics should teach students how to work
with discrete structures, which are the abstract mathematical structures used to
represent discrete objects and relationships between these objects. E.g. sets,
permutations, relations
• Gateway to more advanced courses
• provides the mathematical foundations for many computer science courses including
data structures, algorithms, database theory, automata theory, formal languages,
compiler theory, computer security, and operating systems
Why Mathematics?
Design efficient computer systems.
• How did Google manage to build a fast search engine?
• What is the foundation of internet security?
algorithms, data structures, database,
parallel computing, distributed systems,
cryptography, computer networks…
Logic, number theory, counting, graph theory…
Topic 1: Logic and Proofs
How do computers think?
Logic: propositional logic, first order logic
Proof: induction, contradiction
Artificial intelligence, database, circuit, algorithms
Topic 2: Number Theory
• Number sequence
• (Extended) Euclidean algorithm
• Prime number, modular arithmetic, Chinese remainder theorem
• Cryptography, RSA protocol
Cryptography, coding theory, data structures
Topic 3: Counting
• Sets and Functions
• Combinations, Permutations, Binomial theorem
• Counting by mapping, pigeonhole principle
• Recursions
A B
Probability, algorithms, data structures
Why we are studying this Course? …
• Core Course in CSE
• Has Significant Weightage in GATE Exam.
• A long list of Reasons ….
Few Questions?
• How can a list of integers be sorted so that the integers are in
increasing order?
• How can it be proved that a sorting algorithm correctly sorts a list?
• How many ways are there to choose a valid password on a computer
system?
• How can I encrypt a message so that no unintended recipient can
read it ?
• How can a circuit that adds two integers be designed?
• And many more questions ….
Evaluation Mechanism
Points for Evaluation
• MS Teams Would be used for All Academic Activities (Assignments,
Quizzes, Lecture etc.)
• No Late submission of Assignments allowed.
• Quizzes have a significant Weightage in evaluation
• Attendance would be recorded for each class on MS Teams
• Teacher’s Appraisal marks would depend on your performance in
class.
Other Information
• Will Upload the PDF version of all Text and Referenced Books on MS
Teams, however I will advise all the students to purchase the hard
copy of these books. (You will find these books very useful in the
future course of your study)
• Will Upload other Referenced material on MS Teams time-by-time.
• Students are advisable to have a read on the topic covered to be in
the next class
• Students are advisable to maintain the discipline during the online
interaction. Strict action would be taken for students indulged in
indiscipline behaviour.
Feedback for the Course
• Students need to submit the course feedback twice during the whole
semester.
• The Feedback mechanism would be anonymous.
• First feedback would be during the mid-semester time and the
second one would be around the end of the semester before final
exams.
• Students are encouraged to submit the course feedback for
improvement and analysis purpose.
Questions?
