Discrete Mathematics
In discrete mathematics, items that are isolated or separated in space are studied.
Online
12 WeeksQuick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The completion of a Discrete Mathematics Certification will lay the groundwork for enrolling in higher-level maths courses like real analysis, abstract algebra, maths modelling, geometry, and topology.
Discrete Mathematics Classes shall discuss the symbolic logic techniques which are required for the algebraic understanding of circuits and computer logic and layer introduce you to Boolean algebras with the help of certain examples based on objects.
Discrete Mathematics Certification Syllabus will discuss how to express the overall functioning of a circuit mathematically in terms of certain suitably defined functions called Boolean functions and also consider a simple circuit design problem to illustrate the applications of the relationship between Boolean functions and circuits.
All students get a Discrete Mathematics Certification by MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai under the Swayam Initiative by the Government of India.
The Highlights
- Provided by NMIMS, Mumbai
- Online course
- 12 Weeks course
- Learn at your own pace
- Expert Lectures
Programme Offerings
- video lectures
- Study Materials
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | MPSTME Mumbai |
What you will learn
Discrete Mathematics Certification Course shows differentiating between digital signals (discrete) and analogue signals demonstrates the distinction between discreteness and continuity (continuous). The conceptual complement that discrete mathematics provides to the continuous processes that underpin the study of calculus is suggested by the examples above.
The construction of a circuit for a Boolean expression and the practice of working with mathematical arguments are two things that Discrete Mathematics Training will assist with. It will also aid with the design and simplification of some basic circuits.
The following learning outcomes are achieved upon successful conclusion of this Discrete Mathematics Certification:
- Define and give examples of Boolean algebras, expressions and functions.
- Logic gate operation is represented algebraically.
- Obtain and simplify the Boolean expression representing a circuit.
Who it is for
If the appropriate students apply for the online course Discrete Mathematics, there will be excellent employment prospects like:
Admission Details
Students are urged to enrol in Discrete Mathematics Certification by taking the following measures as soon as the course's admission period opens.
Step 1: Visit the official website
Step 2: Fill up the application form
Step 3: Upload all necessary documents
Step 4: Pay the required fee online (if you need certification)
The Syllabus
Module - 01
- Sets and subsets-Representations-Cardinality-Set operations-Set identities- principle of mathematical induction- principle of inclusion-exclusion
- Assignment - 1
- Deadline – last day of the week
Module - 02
- Ordered sets-languages-phase structure grammars-types of grammars and languages
- Assignment - 2
- Deadline – last day of the week
Module - 03
- Interaction/Discussion on Module 1 & 2 and Assignments
Module - 04
- Basics of counting-permutations-combinations. Pigeon hole principle
- Assignment - 3
- Deadline – last day of the week
Module - 05
- Elements of probability-sample spaces-asssigning probabilities to events-equally likely outcomes
- Assignment - 4
- Deadline – last day of the week
Module - 06
- Interaction\Discussion on Module 4 & 5 and Assignments
Module - 07
- Relations and their properties-binary relations and their applications-representing relations-equivalence relations
- Assignment - 5
- Deadline – last day of the week
Module - 08
- Product sets and partitions-partial orderings-lattices-chains and antichains-functions
- Assignment - 6
- Deadline – last day of the week
Module - 09
- Interaction/Discussion on Module 7 & 8 and Assignments
Module - 10
- Basic definitions and terminology-multigraphs-weghted graphs-paths and circuits
- Assignment - 7
- Deadline – last day of the week
Module - 11
- Shortest paths- Eulerian paths and circuits-Travelling Salesman problem-planar graphs
- Assignment - 8
- Deadline – last day of the week
Module - 12
- Interaction/Discussion on Module 10 & 11 and Assignments
Module - 13
- Definitions-properties-applications of trees
- Assignment - 9
- Deadline – last day of the week
Module - 14
- Spanning trees-minimum spanning trees-applications-Prims and Kruskals algorithm
- Assignment - 10
- Deadline – last day of the week
Module - 15
- Interaction/Discussion on Module 13 & 14 and Assignments
Module - 16
- Finite state machines with output- finite state machines with no output-finite state automata- language recognition by finite state machines-designing finite state automata
- Assignment - 11
- Deadline – last day of the week
Module - 17
- Complexity of algorithms-comparing algorithms-Discrete numeric functions-manipulation of numeric functions-generating functions-operations on generating functions-
- Assignment - 12
- Deadline – last day of the week
Module - 18
- Interaction/Discussion on Module 16 & 17 and Assignments
Module - 19
- Linear recurrence relations- homogeneous and non-homogeneous and solutions
- Assignment - 13
- Deadline – last day of the wee
Module - 20
- Solutions of non-homogeneous type-particular solution and total solution-solution by the method of generating functions
- Assignment - 14
- Deadline – last day of the week
Module - 21
- Interaction/Discussion on Module 19 & 20 and Assignments
Module - 22
- Binary operations-semigroups-products and quotient of semigroups
- Assignment - 15
- Deadline – last day of the week
Module - 23
- Groups- products and quotient groups-other mathematical structures
- Assignment - 16
- Deadline – last day of the week
Module - 24
- Interaction/Discussion on Module 22 & 23 and Assignments
Module - 25
- Lattices and algebraic structures-sub lattices-isomorphic lattices-Principle of duality-special types of lattices-
- Assignment - 17
- Deadline – last day of the week
Module - 26
- Boolean Algebra-Boolean expressions and Boolean functions-identities of Boolean algebra-
- Assignment - 18
- Deadline – last day of the week
Module - 27
- Interaction/Discussion on Module 25 & 26 and Assignments
Module - 28
- Functional completeness-logic gates-exmples of circuits-minimisation of circuits-Karnaugh maps-Quine Mc Clusckey method
- Assignment - 19
- Deadline – last day of the week
Module - 29
- Interaction/Discussion on Module 28 & other modules and Assignments
Module - 30
- Term end assessment:
- Will provide the video answers to the frequently asked questions by the students.
- Interactions and Online evaluation process
Instructors
MPSTME Mumbai Frequently Asked Questions (FAQ's)
Discrete Mathematics plays a significant role in big data analytics, and some examples that use concepts such as Graph theory are Google Maps, encryption and decryption in cryptography
The classes are administered through pre-recorded videos and lectures.
Yes, Discrete mathematics is foundational material for computer science such areas as set theory, logic, graph theory, combinatorics, and probability theory.
The instructor for this course is Dr. Minirani S - Associate Professor in the Department of Basic Sciences and Humanities in NMIMS Deemed University, Vile Parle West, Mumbai.
The various places where it is used includes Distributed Systems, Algorithms, Computer Architecture, Computer Systems, Databases, Functional Programing, Machine Learning, Networks etc..