Essential Geometry Theorems and Properties

Posted by on Mar 15, 2026 in Mathematics | 0 comments

Quadrilaterals

  • The sum of the interior angles of a quadrilateral is 360°.
  • Properties of a parallelogram:
    • Opposite sides are equal.
    • Opposite angles are equal.
    • Consecutive angles are supplementary (sum = 180°).
    • Diagonals bisect each other.
    • A diagonal divides it into two congruent triangles.
  • Conditions for a parallelogram:
    • Both pairs of opposite sides are equal.
    • Both pairs of opposite angles are equal.
    • Diagonals bisect each other.
    • One pair of opposite sides is equal and parallel.
  • Mid-Point Theorem: The line segment
Read More

Solving Polynomial Equations: Descartes and Cardan Methods

Posted by on Mar 12, 2026 in Mathematics | 0 comments

1. Nature of Roots: Descartes’s Rule of Signs

Find the nature of the roots for the equation: x⁴ + 2x² + 3x – 2 = 0

Applying Descartes’ Rule of Signs

Given the function: f(x) = x⁴ + 2x² + 3x – 2

Signs of coefficients: +, +, +, –

Count sign changes:

  • + to + (No change)
  • + to + (No change)
  • + to – (1 change)

Therefore, there is exactly one positive real root.

Replace x with -x:

f(-x) = (-x)⁴ + 2(-x)² + 3(-x) – 2 = x⁴ + 2x² – 3x – 2

Signs: +, +, -, –

Count sign changes:

  • + to + (No change)
  • + to – (1 change)
Read More

Refractive Index Determination: Glass Slab and Prism Experiments

Posted by on Mar 11, 2026 in Mathematics | 0 comments

Experiment 6: Refractive Index Determination

Part 1: Refractive Index of a Glass Slab (Pin Method)

Aim

To determine the refractive index of a glass slab material using the pin method.

Apparatus and Materials

Glass slab, drawing board, drawing pins, hairpins, paper, scale, and protractor.

Theory

The refractive index, n, of glass with respect to air is defined by Snell’s Law:

n = sin i / sin r

where i is the angle of incidence and r is the angle of refraction.

A graph plotted with sin r along the X-axis and

Read More

Essential Excel Formulas and Functions Reference

Posted by on Mar 11, 2026 in Mathematics | 0 comments

Quick Reference: Excel Formulas

  • Adding many cells: =SUM
  • Adding 2 cells: + or –
  • Finding typical value: =AVERAGE
  • Finding true middle: =MEDIAN
  • Finding smallest: =MIN
  • Finding largest: =MAX
  • Counting numbers: =COUNT
  • Counting text or anything: =COUNTA
  • Applying rule/condition: =IF
  • Calculating loan payment: =PMT
  • Summarizing multiple sheets: 3D SUM
  • Testing different scenarios: Goal Seek / Data Table
  • Multiplying by fixed %: Absolute reference ($)

1. Mathematical & Statistical Functions

These are the workhorses of Excel

Read More

Core Epidemiology Concepts: Definitions, History, and Measures

Posted by on Mar 4, 2026 in Mathematics | 0 comments

Lectures 1–2 – Intro to Epidemiology

Key Definitions:

Epidemiology: study of frequency, distribution, determinants of health/disease in populations + application to control.
Frequency: how often events occur (counts, proportions, rates).
Distribution: patterns by person/place/time.
Determinants: factors influencing occurrence (host/agent/environment).

Historical Figures (name + contribution):

  • Edward Jenner: cowpox → smallpox vaccine (1st vaccination).

  • James Lind: scurvy + citrus trial.

  • Percival Pott:

Read More

Discrete Mathematics: Sets, Graphs, and Matrix Algebra

Posted by on Feb 23, 2026 in Mathematics | 0 comments

Unit 1: Set Theory and Functions

1. Set

A set is a well-defined collection of distinct objects, called elements or members. These objects can be numbers, symbols, people, or even other sets. Sets are usually denoted by capital letters such as A, B, or C, and their elements are written within curly braces. For example, A = {1, 2, 3}. A set must be well-defined, meaning it should be clear whether a given object belongs to the set or not. Sets play a foundational role in mathematics and computer science

Read More