Mathematics Notes
Subject Overview
The opening paper of M.Sc IT rebuilds the discrete-math foundation the program's computing papers assume — number systems and radicals, set theory and its operations, propositional logic, and matrix algebra. A compact refresher paper covering representation, formulas and basic operations rather than advanced theory. A 4-credit core theory paper.
Subject at a glance
2
Units
19
Topics
4
Credits
2
Infographics
Unit-wise Syllabus
2 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- Natural
- integer
- real
- rational and irrational numbers
- sums and products of rational numbers
- integer exponents
- radicals (square and cube roots and their simplification)
- set representation (roster and set-builder methods)
- types of sets (null, singleton, finite, infinite, equal, equivalent, disjoint, subset, power set, universal set)
- set operations (union, intersection, difference, symmetric difference, complement)
Rational
Can be written as p/q: 3/4, −2, 0.5
Integers
…, −2, −1, 0, 1, 2, …
Whole numbers
0, 1, 2, …
Natural numbers
1, 2, 3, …
Irrational
Non-terminating, non-repeating: √2, π
Study guide
This bridging unit revises the number systems (natural, integer, rational, irrational and real numbers), exponents and radicals and sets: representation, types and operations including symmetric difference and complement. Use Venn diagrams to check every set operation.
- Logic statements and connectives
- basic logic operations (conjunction, disjunction, negation)
- logical equivalence
- tautologies and contradictions
- types of matrices (row, column, rectangular, square, diagonal, scalar, unit, triangular, null)
- matrix algebra — scalar multiplication
- addition
- subtraction
- multiplication and transpose
p ∧ q (conjunction)
F
F
p ∨ q (disjunction)
T
T
¬p (negation)
F
T
p → q (implication)
F
T
Study guide
You study logic statements, connectives, conjunction, disjunction, negation, equivalence, tautologies and contradictions, and matrix types and algebra: addition, multiplication, scalar multiplication and transpose. Build truth tables for every logic problem and practise multiplying matrices carefully.
Why Mathematics Matters
This paper brings students from different undergraduate backgrounds to a common base in discrete mathematics, which supports algorithms, databases and machine learning in later semesters.
How to Prepare for Mathematics
- Practise set, logic and matrix problems until they are routine.
- Revise from the earlier unit on number systems if your base is weak.
- Use truth tables and diagrams as checks.
Mathematics: Frequently Asked Questions
Why does M.Sc IT include basic mathematics?
Students come from varied backgrounds, so this paper gives everyone the same grounding in sets, logic and matrices needed for advanced computing topics.