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Saturday, December 21, 2024

TEACH YOURSELF PROBABILITY AND STATISTICS WITH PERVEZ HOODBHOY

Languages: Urdu, English
These are self-study lectures on probability theory suitable for college level students studying mathematics, physics, economics, and business.  
Module 1.1 (English, Urdu)
  • Random experiments, sample space and events, A quick review of sets, Venn diagrams and consequences, Sample space and events — examples, Axioms of probability, Probability — elementary examples
Module 1.2 (English, Urdu)
  • Factorials and their applications, Pascal’s Triangle, Counting outcomes, Conditional probability, Worked examples of conditional probability, Probability trees, Bayes’ Rule
Module 1.3 (English, Urdu)
  • Random variables, Geometric random variable, Binomial random variable, Expectation (mean) values, Worked examples. Poisson random variable, Call centre problem
Module 1.4 (English, Urdu)
  • Variance and standard variation, E[X] and E[X^2] for binomial distribution, The Chebyshev Rule, Cumulative Distribution Function, Continuous random variables, Connecting discrete to continuous probabilities, Examples of continuous probability distributions
Module 1.5 (English, Urdu)
  • Covariance and Correlation, Some simple properties of covariance, A physical understanding of covariance, Several discrete random variables, Illustrative solved examples
Module 1.6 (English, Urdu)
  • Two continuous random variables, Some basic formulae, Practice with double integrals, Example: trains arriving at a station, Example: aiming darts at a board, Example: Buffon’s needle
Module 1.7 (English, Urdu)
  • A function of generating moments, Example: Binomial Distribution, Example: Poisson Distribution, Example: Exponential Distribution, Introduction to Normal Distribution, Binomial Distribution Normal Distribution (proof), Law of Large Numbers (with proof)
Module 1.8 (English, Urdu)
  • Central Limit Theorem – with potatoes, CLT – why it is astonishing, Generating moments of the normal distribution, Generating moments for n independent variables, Proof of CLT, CLT for i.i.d’s that are uniformly distributed, CLT – three applications
Module 1.9 (English, Urdu)
  • One-dim drunkard’s walk – a first look, Random walk definitions, First return theorem, The eventual return problem, Random walk in two dimensions
Module 1.10 (English, Urdu)
  • States, Transitions, Markov Chains, Three examples of Markovian processes, Markovian basics, Regular (ergodic) Markov Chains, Absorbing Markov Chains
Recommended textbooks and materials:

  1. A Natural Introduction to Probability Theory, Robert Meester, Birkhäuser Verlag (2008).
  2. Introduction to Probability Models, 9th Edition, Elsevier (2009).
  3. Grinstead and Snell’s Introduction to Probability, the CHANCE Project (2006).
  4. Probability Theory and its Applications, William Feller, 3rd edition, John Wiley (1970).
For worked examples, I strongly recommend the books by Hossein Pishro-Nik which you can easily locate with a Google search.

TEACH YOURSELF THERMODYNAMICS WITH PERVEZ HOODBHOY

Languages: Urdu, English
These lectures are suitable for undergraduate level teaching (years 16-20) and provide the conceptual foundations of thermodynamics. Although several examples are worked out here, for a fuller grasp of the subject students should work out at least some problems in the texts recommended below.  
Module 1.1 (English, Urdu)
  • Heat, temperature, zero’th Law of thermodynamics, thermometers, absolute zero, third law of thermodynamics
Module 1.2 (English, Urdu)
  • Conversion of energy from one form to another, units of heat and energy, internal energy (example: ideal gas), thermodynamic variables and equation of state, isolated, closed and open systems, first law of thermodynamics (circa 1840), exact and inexact differentials
Module 1.3 (English, Urdu)
  • Adding heat to a system, various heat capacities of a substance, enthalpy and its uses, moles: a quick reminder from chemistry, measuring heat capacities, heat capacities of a non-ideal gas
Module 1.4 (English, Urdu)
  • Reversible and irreversible processes, isothermal expansion of a gas, adiabatic expansion of a gas, free expansion of a gas, application: speed of sound
Module 1.5 (English, Urdu)
  • Entropy – a qualitative understanding, entropy – formal definition, entropy as a state function, thermodynamic cycles, worked example
Module 2.1 (English, Urdu)
  • Heat engines and efficiency, carnot engine, second law of thermodynamics, equivalence between Clausius and Kelvin statements, the Carnot engine is universal – proof, analyzing the Carnot engine, solved example
Module 2.2 (English, Urdu)
  • Absolute temperature defined, the Clausius inequality – derivation, consequences of the Clausius inequality, why the entropy of the universe has to increase, using entropy as a state variable, solved example I, solved example II
Module 2.3 (English, Urdu)
  1. Helmholtz free energy, Gibbs free energy, application to chemical reactions, melting and Gibbs free energy, open systems and Gibbs free energy, chemical potential – physical interpretation, chemical potential for an ideal gas
Module 2.4 (English, Urdu)
  • Examples of phase transitions, melting of ice – worked example, Euler’s theorem and molar quantities, Clausius-Clapeyron equation – derivation, phase diagrams, first and second order phase transitions
Module 2.5 (English, Urdu)
  • Black body radiation, planetary temperatures from Stefan-Boltzman Law, radiation pressure, entropy of a photon gas, thermodynamics of the expanding universe
Recommended textbooks and materials:
  1. Feynman Lectures in Physics – chapters 44, 45, 46
  2. Principles of Thermodynamics, Jean-Philippe Ansermet and Sylvain D. Brechet
  3. Essential Classical Thermodynamics, Ulf W. Gedde
  4. Problems and Solutions on Thermodynamics and Statistical Mechanics, World Scientific

TEACH YOURSELF WAVES AND OSCILLATIONS WITH PERVEZ HOODBHOY

GOAL
To enable students to learn this beautiful subject with zero or minimal assistance.
LECTURES
(More units will be added one by one. Stay connected.)

TEACH YOURSELF QUANTUM MECHANICS WITH PERVEZ HOODBHOY

GOAL
To enable students to learn this beautiful subject with zero or minimal assistance.
LECTURES

TEACH YOURSELF SPECIAL RELATIVITY WITH PERVEZ HOODBHOY

GOAL
To enable students to learn this beautiful subject with zero or minimal assistance.
CONTENTS AND INSTRUCTIONS
Click here to download the contents and instructions for this series of 8 self-learning lectures by Pervez Hoodbhoy.
LECTURES

TEACH YOURSELF CALCULUS WITH PERVEZ HOODBHOY

GOAL
To enable students to learn this beautiful subject with zero or minimal assistance.
CONTENTS AND INSTRUCTIONS
Click here to download the contents and instructions for this series of 30 self-learning lectures by Pervez Hoodbhoy.
LECTURES

TEACH YOURSELF PHYSICS WITH PERVEZ HOODBHOY

Click here for accompanying Notes for Video Lectures (1-45) below:
BONUS LECTURES
NON-LINEAR

MISSION STATEMENT

The Eqbal Ahmad Centre for Public Education (EACPE) seeks to foster the use of science and reason to understand nature and society and so better enable all citizens of Pakistan to participate fully in the political, social, economic, and cultural life of their society; to exercise their democratic rights and responsibilities; to value human rights, democracy and the rule of law; to promote cultural and religious diversity; to raise awareness of global issues and the natural environment; and to advance the goals of international peace and justice.

EACPE is named to honour the life and work of distinguished Pakistani academic, activist, and public intellectual, Dr. Eqbal Ahmad.

TEACH YOURSELF SERIES

A NOTE FROM NOAM CHOMSKY

“The EACPE record is very impressive, and hopeful — a rarity these days. About the webpage (design), I don’t have anything useful to say. Have little experience that’s relevant. To me personally, the range and choice of topics is appealing and impressive. I can’t think of any useful way to improve it.”

— Noam

(Received on 5th May, 2017. As a member of the EACPE board, Professor Noam Chomsky was asked to suggest how to improve our main page)

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