The fast pace of the UBC MM program means that all students will need to have a foundational proficiency in Quantitative Methods and familiarity with Statistics and Economics. When your classes begin in September, you’ll need to be familiar with all of the material listed below as classes move along very quickly.
Each of you comes to the program with a different academic background, so your familiarity with the academic prep tutorials will also vary. It may be that some of the resources on this list are very familiar to you, and you can quickly review them to make sure you’re up to speed, or you may have never covered some of the subjects and will need to learn them in-depth.
Instructions
Where to begin: Review each section and complete those areas you are currently not comfortable with. Most tutorials include quizzes and practice tests, so completing these is a good way to quickly review if you are familiar with the content.
If you'd like to track your learning progress you can sign up for a user account with Khan Academy, but it's not required.
Completion times: We have estimated the amount of time to complete each section based on the length of videos and allocating time for the practice questions. It may take you longer or shorter than we have indicated and after a few sections you'll begin to get an idea of your speed compared to our estimates.
Disclaimer: These tutorials have not been vetted in-depth. They have been selected based on the concepts included and tutorial descriptions. You are encouraged to explore the content and cover concepts you are unfamiliar with. The aim is to ensure that you have foundational proficiency in these topics, but not all concepts may apply directly to course work.
All resources are from Khan Academy, unless otherwise indicated.
If you have feedback about these academic prep materials, please let us know.
Arithmetic & Excel
ARITHMETIC
Relevant for Statistics, Operations, Finance, Economics.
The Basic Order of Operations (PEMDAS) (20 mins)
Fractions (approx. 1 hour 15 mins total)
- Introduction to Fractions (15 mins)
- Equivalent Fractions (40 mins)
- Simplifying Complex Fractions (20 mins)
Averages (9 mins total)
Modeling with Linear Equations (10 mins)
MICROSOFT EXCEL
30 mins to 2 hours approximate study time, depending on previous skill level. Relevant for Statistics, Operations, Finance.
- Excel training (delivered by Microsoft)
Skip any sections you are already familiar with
Algebra
19 hours approximate study time. Relevant for Statistics, Operations, Finance, Economics.
General
Functions (approx. 1 hour 20 mins total) (Relevant for Economics)
- Maximum and minimum points (15 mins)
- Average rate of change (30 mins)
- Average rate of change word problems (35 mins)
Logarithms (approx. 45 mins total) (Relevant for Economics & Finance)
Introduction to Algebra (approx. 3 hours 50 mins total) (Relevant for Statistics/Operations)
- Overview and history of algebra (35 mins)
- Introduction to variables (25 mins)
- Substitution and evaluating expressions (15 mins)
- Evaluating expressions word problems (15 mins)
- Writing algebraic expressions introduction (23 mins)
- Dependent & independent variables (10 mins)
- Combining like terms (32 mins)
- Introduction to equivalent algebraic expressions (7 mins)
- Interpreting linear expressions (10 minss)
- Division by zero (15 mins)
- Unit test (25 mins)
One-variable linear equations (approx. 5 hours total) (Relevant for Statistics/Operations)
- Algebraic equations basics (23 mins)
- Why we do the same thing to both sides of an equation (15 mins)
- One-step addition & subtraction equations (25 mins)
- One-step multiplication & division equations (40 mins)
- Two-steps equations intro (20 mins)
- Two-step equation word problems (20 mins)
- Linear equations with variables on both sides (35 mins)
- Linear equations with parentheses (20 mins)
- Analyzing the number of solutions to linear equations (18 mins)
- Linear equations word problems (25 mins)
- Linear equations with unknown coefficients (10 mins)
- Unit test (25 mins)
One-variable linear inequalities (approx. 1 hour 10 mins total) (Relevant for Statistics/Operations) (only sections indicated below)
- Introduction to inequalities with variables (40 mins)
- One-step inequalities (20 mins)
- Quiz 1 (10 mins)
Two-variable linear equations (approx. 6 hours 50 mins) (Relevant for Statistics/Operations)
- Two-variable linear equations intro (30 mins)
- x-intercepts and y-intercepts (40 mins)
- Slope (50 mins)
- Horizontal & vertical lines (20 mins)
- Intro to slope-intercept form (30 mins)
- Graphing slope-intercept equations (25 mins)
- Writing slope-intercept equations (50 mins)
- Point-slope form (30 mins)
- Standard form (35 mins)
- Summary: Forms of two-variable linear equations (35 mins)
- Unit test (30 mins)
Ratio, Proportion, & Percent
2 hours 20 mins approximate study time. Relevant for Finance.
Ratio, Proportion and Percent
- Introduction to Ratios (30 mins)
- Solving Percent Problems (10 mins)
Accounting & Financial Statements
- Cash versus accrual accounting (13 mins)
- Three core financial statements (27 mins)
Statistics
11 hours 40 mins approximate study time. Relevant for Statistics/Operations.
Displaying & Describing Data (approx. 6 hours 50 mins total) (only sections indicated below)
- Categorical data displays (20 mins)
- Two-way tables for categorical data (35 mins)
- Histograms (15 mins)
- Line graphs (6 mins)
- Mean and median: The basics (45 mins)
- Range, Interquartile range (IQR) - just Range & IQR (no MAD) (15 mins)
- Population variance and standard deviation (1 hour 15 mins)
- Variance and standard deviation of a sample (1 hour 45 mins)
- Unit test (30 mins)
Modelling Data Distributions (approx. 3 hours 15 mins total)
- Percentiles (12 min)
- Z-Scores (12 min)
- Effects of Linear Transformations (10 min)
- Density curves (25 min)
- Normal distributions (2 hours 10 mins)
Probability (approx. 1 hour 25 mins total) (only sections below)
- About (1 min)
- Basic theoretical probability (50 mins)
- Probability using sample spaces (20 mins)
- Quiz #1 (15 mins)
Probability Distributions
- Constructing a Probability Distribution (7 mins)
- Calculating Conditional Probability (7 mins)
Sampling Distributions (approx. 35 mins total) (only sections below)
- Central limit theorem (10 mins)
- Sampling distribution of the sample proportion (11 mins)
- Sampling distribution of the sample mean (2 – 14 mins)
Economics
Economics - 10 hours approximate study time. Relevant for Economics.
We will take for granted knowledge of basic algebraic manipulations, including simplifying single equations for the value of a variable in terms of other parameters and solving two-equation, two-variable problems. We will also assume students are familiar with moving between algebraic and graphical representations of functions of two variables (most importantly, straight lines). Differential calculus will be used in some optimization problems, and students should be familiar with techniques of differentiation for polynomials and exponential functions, in particular. Parts of our course deal with situations of uncertainty, and for this reason it is helpful for students to be familiar with the basics of probability theory, and the concepts of expected value and variance, in particular.
Economics-specific concepts to know include the following: opportunity cost; marginal cost and marginal revenue; elasticity; demand curve; (industry) supply curve; Nash equilibrium
- Intro to Economics: Crash Course Econ #1 (13 mins) (Youtube video)
Average costs (ATC, MC) and marginal revenue (MR)
- Marginal cost and average total cost (7 mins)
- Marginal revenue and marginal cost (6 mins)
- Marginal revenue below average total cost (6 mins)
Differential Calculus
Derivative introduction (approx. 3 hours 45 mins total)
- Introduction to differential calculus (35 mins)
- Derivative as slope of tangent line (15 mins)
- Derivative as instantaneous rate of change (20 mins)
- Secant lines (45 mins)
- Derivative as a limit (25 mins)
- Formal definition of derivative (20 mins)
- Differentiability (27 mins)
- Derivative as a function (25 mins)
- Review: Derivative basics (15 mins)
Basic differentiation (approx. 2 hours 15 mins total)
- Basic differentiation rules (40 mins)
- Power rule (23 mins)
- Polynomial functions differentiation (45 mins)
- Review: Basic differentiation (30 mins)
Product, quotient & chain rules (approx. 1 hour 35 mins total)
- Product rule (45 mins)
- Chain rule (50 mins)
Derivative applications (approx. 1 hour 40 mins total) (only section below)
- Optimization (1 hr 40 mins)
Game theory and Nash Equilibrium (approx. 17 mins total)
- Prisoner’s dilemma and the Nash equilibrium (10 mins)
- More on Nash equilibrium (7 mins)