Jiajun Zhang

Jiajun Zhang

He/Him

M.Sc in Statistics

Math Resources

In this page, you will find several notes on different mathematics topics, notes were mainly taken from my undergraduate classes and I have organised them into different topics. It contains notes on calculus, linear algebra, real analysis, differential equations, probability theory, and statistical inferences. To report a typo, please send me an email.

Regression and Analysis of Variance

This note is based on MATH 533 (Regression and ANOVA) at McGill University taught by Prof. Mehdi Dagdoug, where my notes can be found here

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Regression and ANOVA

Written in Winter, 2025

Please consult my notes here: here

Recommended citation: Jiajun Zhang, (2025) Regression and ANOVA Course Notes

Generalized Linear Models

This note is based on MATH 523 (Generalized Linear Models) taught by professor Russell Steele at McGill University, in Winter 2026. My notes (will be updated weekly): here

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Statistics

This note is based on MATH 357 (Honors Statistics) at McGill University taught by Prof. Abbas Khalili. A summary of the topics covered in this class: (here). The complete set of notes: (here), which is still under construction so far.

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Random Samples

Written in Winter, 2025

We will investigate some basic theories of random samples

Recommended citation: Jiajun Zhang, (2025) Random Samples

Unbiased Estimators

Written in Winter, 2025

We will investigate some basic theories of unbiased estimators

Recommended citation: Jiajun Zhang, (2025) Unbiased Estimators

Uniformly Minimum Variance Unbiased Estimator (UMVUE)

Written in Winter, 2025

We will investigate some basic theories of Uniformly Minimum Variance Unbiased Estimator (UMVUE)

Recommended citation: Jiajun Zhang, (2025) Uniformly Minimum Variance Unbiased Estimator (UMVUE)

Theory of Sufficiency

Written in Winter, 2025

We will investigate some basic theories of sufficiency

Recommended citation: Jiajun Zhang, (2025) Sufficiency

Confidence Interval

Written in Winter, 2025

In this article we will talk about confidence interval

Recommended citation: Jiajun Zhang, You. (2025), part of my notes in Honors Statistics taught by Prof. Abbas Khalili

Hypothesis Testing

Written in Winter, 2025

We will investigate basic theories of hypothesis testing

Recommended citation: Jiajun Zhang, (2025) Hypothesis Testing

Probability

This note is based on MATH 356 (Honors Probability) at McGill University taught by Prof. Masoud Asgharian. My Notes: (my own notes here)

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Conditional Probability and Bayes Theorem

Written in Fall, 2024

We will investigate conditional probability and Bayes theorem.

Recommended citation: Jiajun Zhang, (2024) Conditional Probability and Bayes Theorem

Random Variables and Distributions

Written in Fall, 2024

We will investigate random variables and its density function, probability distribution.

Recommended citation: Jiajun Zhang, (2024) Random Variables and Distributions

Moments, Generating Functions and Inequalities

Written in Fall, 2024

We will investigate moments of a random variable, and generating functions, and some inequalities related to moments.

Recommended citation: Jiajun Zhang, (2024) Moments, Generating Functions and Inequalities

Some Discrete Random Variables

Written in Fall, 2024

We will investigate some famous discrete random variables

Recommended citation: Jiajun Zhang, (2024) Some Discrete Distributions

Some Continuous Random Variables

Written in Fall, 2024

We will investigate some famous continuous random variables

Recommended citation: Jiajun Zhang, (2024) Some Continuous Distributions

Multiple and Independent Random Variables

Written in Fall, 2024

We will investigate multiple random variables and independent random variables

Recommended citation: Jiajun Zhang, (2024) Multiple and Independent Random Variables

Conditional Distributions

Written in Fall, 2024

We will investigate conditional distributions

Recommended citation: Jiajun Zhang, (2024) Conditional Distributions

Covariance and Correlations

Written in Fall, 2024

We will investigate covariance and correlations

Recommended citation: Jiajun Zhang, (2024) Covariance and Correlations

Convergence Theorems

Written in Fall, 2024

We will investigate convergence theorems

Recommended citation: Jiajun Zhang, (2024) Convergence Theorems

Calculus

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Solving Trigonometric Integrals

Written in Summer, 2024

In this article we will investigate different ways to solve trigonometric integrals

Recommended citation: Jiajun Zhang, (2024). Solving Trigonometric Integrals

Partial Fraction Decompositions

Written in Summer, 2024

In this article we will investigate different ways to solve integrals which is a fraction of two polynomials

Recommended citation: Jiajun Zhang, (2024). Partial Fractions Decompositions

Testing Series

Written in Summer, 2024

In this article we will investigate different ways to test the convergence of series

Recommended citation: Jiajun Zhang, (2024). Testing Series

Partial Differential Equations

This note is based on MATH 475 (Honors PDE) at McGill University taught by Prof. Adam Oberman. My notes: here

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Harmonic Functions

Written in Summer, 2025

In this article we will investigate some properties of harmonic functions and fundamental solutions to the Laplace equations.

Recommended citation: Jiajun Zhang, (2025). Harmonic Functions
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Linear Algebra

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Real Analysis

Here you can find my notes on a higher-level analysis course. It was taught by Prof. Linan Chen at McGill University during Fall 2024.

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Honors Analysis 3 Notes

Written in Fall, 2024

This is a note on analysis

Recommended citation: Jiajun Zhang, (2024) Honors Analysis 3 Notes

Complex Analysis

This note is based on MATH 249 (Honors Complex Analysis) taught by professor Henri Darmon at McGill University, in winter 2026. My notes (will be updated weekly): here

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Complex Analysis

Written in Winter, 2026

My notes: here

Recommended citation: Jiajun Zhang, (2026) Honors Complex Analysis Notes

Ordinary Differential Equations

This note is based on MATH 325 (Honors ODE) at McGill University taught by Prof. Jean-Philippe Lessard. My notes: here

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Ordinary Differential Equations

Written in Winter, 2025

Please consult my notes here: here. Note that some topics are not covered in this note. They are under construction, and I will try my best tp update.

Recommended citation: Jiajun Zhang, (2025) Honors ODE (MATH 325) Course Notes

Discrete Mathematics and Graph Theory

This note is based on MATH 350 (Honors Discrete Mathematics) at McGill University.

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Graph Theory Exercise Bank

Written in Fall, 2025

I have listed many nice exercises in Graph Theory. Most of them are taken from past midterm exams and assignments

Recommended citation: Jiajun Zhang, (2025) Graph Theory Exercise Bank