Computational Mathematics - Complete Study Notes

This folder supports two different ways to study Computational Mathematics for MCA Semester I:

1. Guided beginner lessons teach prerequisites in small concept blocks with intuition, examples, checkpoints, programming links, and practice.
2. University module notes are compact exam references for the official six modules. A module is not intended to be completed as one short lesson.

Each module follows three learning layers:

1. Simple idea: plain language and a familiar analogy.
2. Worked example: a small, step-by-step problem.
3. Technical meaning: correct definitions, tables, and exam points.

A small running example is reused across modules to keep ideas consistent: the Campus graph for graph theory, a fixed 2x2 / 3x3 matrix example for linear algebra, and small propositions p, q, r for logic.

Beginner Learning Path

This path builds mathematical prerequisites before the university modules. Each lesson uses plain English, analogies, worked problems, programming connections, and practice checkpoints. Complete only one concept block at a time and check your answer before continuing.

Lesson	Topic	Status
1	Algebra Review - Building the Foundation	Available
2	Functions and Coordinate Graphs	Continue after completing Lesson 1
3	Powers, Logarithms, Limits, and Basic Calculus	Planned prerequisite
4	Matrices and Determinants	Planned
5	Systems of Linear Equations	Planned
6	Vectors	Planned
7	Eigenvalues and Eigenvectors	Planned
8	Numerical Methods and Interpolation	Planned
9	Numerical Differentiation and Integration	Planned
10	Probability	Planned
11	Statistics	Planned
12	Graph Theory and Discrete Mathematics	Planned
13	Optimization	Planned

Complete the checkpoints and exercises in one lesson before moving to the next.

Module-wise study method

1. Review the module prerequisites and learning outcomes.
2. Complete one 10-15-minute study block at a time.
3. Rework calculations without looking at the example.
4. Attempt the mini quiz and practice ladder before revealing solutions.
5. Mark the module Mastered only after scoring at least 80% without notes.

Module Index

Module	Topic	File
1	Logic: propositional and predicate calculus, Boolean algebra, natural deduction	Module 1
2	Well-formed formulae and computable type checking	Module 2
3	Graphs and trees: terminology, MST, Eulerian walking	Module 3
4	Matrices: operations, algebra, geometric interpretation	Module 4
5	Vector spaces and subspaces: bases, independence, transformations	Module 5
6	Eigenvalues and eigenvectors, similarity, geometric interpretation	Module 6

Deep-Dive Articles

Module	Article
1	Module-1-Article
2	Module-2-Article
3	Module-3-Article
4	Module-4-Article
5	Module-5-Article
6	Module-6-Article

Revision Tools

• Quick Revision - last-minute review of all modules.
• Cheat Sheet - rules, formulas, and procedure summaries.
• Important Questions - exam questions with answer points.
• MCQ - multiple-choice practice by module.
• Glossary - important terms in alphabetical order.
• Web Resources - official and high-quality external references.
• PDF-Based Study Notes - consolidated notes from the available Modules 1-4 PDFs.
• Internal Exam 1 - 23-question paper with 8 sections and answer key.
• Practice Test 1 - revision test for Modules 1-2.
• Practice Test 2 - revision test for Modules 3-4.

How to use this folder

1. Read the matching module note first.
2. Open the matching article for a deeper explanation and extra examples.
3. Use the cheat sheet for fast revision of formulas.
4. Practice the MCQs and important questions without looking at the notes.

Running examples

• Logic: p = "It is raining", q = "The ground is wet", r = "I carry an umbrella".
• Graph: the Campus graph G = ({A,B,C,D,E}, {AB, BC, CD, DE, EA, AC}) with weights, used for spanning tree and MST.
• Matrices: M = [[2,1],[1,2]] and A = [[1,2,3],[0,1,4],[5,6,0]] reused for determinant, inverse, and eigenvalue work.