MAKAUT Discrete Mathematics Organizer | PCC-CS-401

1. 01

   Probability Theory & Distributions

   3 points

   • Fundamental Concepts and TheoremsDefines axiomatic probability, Bayes' Theorem, and conditional probability formulations.
   • Common Probability DistributionsCovers Discrete (Binomial, Poisson) and Continuous (Uniform, Exponential, Normal) distributions alongside their expected values, means, and variances.
   • Limit TheoremsExplains the Central Limit Theorem and Chebyshev's (Tchebycheff's) Inequality for approximating probabilities of random variables.
2. 02

   Mathematical Statistics & Hypothesis Testing

   2 points

   • Estimation TheoryExamines point and interval estimation, maximum likelihood estimators (MLE), and properties like unbiasedness and consistency.
   • Sampling & TestingDetails sampling distributions, null/alternative hypotheses, Type I and Type II errors, $z$-tests, $t$-tests, and Chi-square ($\chi^2$) goodness-of-fit tests.
3. 03

   Advanced Graph Theory

   2 points

   • Planar Graphs & DualsDiscusses planarity conditions, Euler's formula ($n - e + f = 2$), Kuratowski's graphs, and rules for constructing dual graphs.
   • Coloring & Eulerian PathsDetails graph coloring, chromatic numbers, chromatic polynomials for trees/circuits, and conditions for Eulerian circuits.
4. 04

   Group Theory

   2 points

   • Group StructuresDefines groups, abelian/commutative groups, subgroups, normal subgroups, quotient groups, and cyclic groups.
   • Group Theorems & MappingsExplores Lagrange's theorem, symmetric/dihedral groups, permutation groups, and mappings including homomorphisms, isomorphisms, and kernels.
5. 05

   Rings & Fields

   2 points

   • Algebraic SystemsDefines rings, subrings, ideals, integral domains, zero divisors, and fields.
   • Key PropertiesEstablishes that every finite integral domain is a field, cancellation laws hold in rings without zero divisors, and field equations possess unique solutions.

Why use this organizer?

• A concise summary of the concepts, for quick revision.
• Covers important topics from the MAKAUT syllabus.
• Organised so you can study efficiently, topic by topic.
• Ideal for last-minute preparation before semester exams.