Tepper · MS in Business Analytics Course
I built

MS in Business Analytics Math Skills Workshop

The math incoming MS in Business Analytics students need before the quantitative core begins.

A workshop I developed for incoming MS in Business Analytics students in Summer 2026. The goal is for students to start the program's quantitative courses with the mathematics already in place, so they are not learning it at the same time as the statistics.

Summer 2026
Self-paced online, on Canvas

Slide: The Daily Grind: $4,500 a month in fixed costs and a $5 cup. When does it break even?

Slide: Weighted averages: watch time by subscriber tier

Slide: Does Hospital A match the 50-minute national benchmark?

slides from the decks
I taught from

Summer 2026 · Self-paced online, on Canvas

Week by week

Scroll the schedule and the slides follow along: five from each session, picked from the decks I taught from.

Module 1: Algebra Fundamentals and Functions
Lesson 1.1M1Solving Linear Equations and Isolating VariablesRunning case: The Daily Grind, a coffee shop $The Daily Grind: $4,500 a month in fixed costs and a $5 cup. When does it break even?$ $The golden rule: whatever you do to one side, do to the other$ $Translating words into algebra: cost and revenue as functions of cups sold$ $Solving 4,500 + 1.50x = 5.00x step by step: about 1,286 cups a month$ $Rearranging Revenue = Price × Quantity to answer the boss's new question$
Lesson 1.2M1Solving Quadratic Equations $Demand Q = 200 − 20P: at what price does the shop bring in $400 a day?$ $Factoring, the fast method when the numbers cooperate$ $The quadratic formula gives two prices that produce the same revenue$ $The discriminant tells you how many solutions exist before you solve$ $The vertex of the revenue curve is the revenue-maximizing price$
Lesson 1.3M1Proportions and Percentages $Profit margin, markup, and conversion rate: three formulas students will use constantly$ $Every percentage problem is a rearrangement of Part = Rate × Whole$ $Reversing a 15% increase means dividing by 1.15, not subtracting 15%$ $Weighted averages: blending $18 and $10 beans to hit $13 a pound$ $Funnel math: 2,000 visitors, 600 free trials, 120 paid subscribers$
Lesson 1.4M1Functions and Graphs $A function is a machine: one input in, exactly one output out$ $Linear in action: the shop's profit is P(x) = 3.50x − 4,500$ $Polynomial in action: cut the price to sell more and revenue curves over$ $Average cost per cup falls toward $1.50 but never reaches it$ $Piecewise functions: a bulk discount changes the rule past a threshold$
Lesson 1.5M1Exponential and Logarithmic Functions $Exponential growth, y = a·bᵗ, sketched by hand$ $The natural base e: what compounding becomes when it is continuous$ $Two logs that matter: ln for continuous growth, log₁₀ for orders of magnitude$ $Logs turn an exponential curve into a straight line$ $Reading a log scale: equal spacing means equal multiplication$
Lesson 1.6M1Algebra in Action: Applications to Analytics $Multi-product break-even: coffee and pastries in one equation$ $Why log-transform: in ln Q = a + b ln P, the slope b is the price elasticity$ $Growth rate from $120K to $156K in two years, using logarithms$ $The algebra behind linear regression: slope and intercept from sums$ $Log scales let GDP per capita from $500 to $80,000 fit on one axis$
Module 2: Calculus Essentials for Analytics
Lesson 2.1M2Derivatives and Rates of ChangeRunning case: NovaSilicon, an AI chip maker $Average rate of change in profit between two production levels$ $The derivative is the slope of the tangent line$ $What the derivative tells the business: expand, cut back, or stop at the peak$ $The chain rule is how a neural network passes gradients back through its layers$ $Gradient descent: follow the slope down to the lowest loss$
Lesson 2.2M2Optimization and Critical Points $NovaSilicon's pricing challenge: where is the peak of the profit curve?$ $A critical point is where the tangent goes flat$ $The second-derivative test: concave down spills water, concave up holds it$ $Inflection points on a technology adoption curve$ $Training a model is optimization: set dL/dw to zero and check the curvature$
Lesson 2.3M2Applications to Analytics Models $Predicting chip yield from fabrication temperature$ $Loss as the sum of squared residuals$ $Gradient descent: rolling downhill on the loss surface$ $Logistic regression: the sigmoid turns a score into a probability$ $Data, model, loss, gradient, update, repeat: the loop behind modern machine learning$
Lesson 2.4M2Partial Derivatives $NovaSilicon sells two chip lines, so profit now has two inputs$ $A function of two variables is a surface$ $To take ∂f/∂x, treat every other variable as a constant$ $The gradient points uphill, in the direction of steepest ascent$ $Real models have millions of parameters, each with its own partial derivative$
Lesson 2.5M2Integration Basics $A wafer line ramps up, then drifts down: how many chips in a 10-hour shift?$ $Integration reverses differentiation$ $A definite integral is the area under the curve$ $The Fundamental Theorem of Calculus: F(b) − F(a)$ $Same machinery, different question: probability as area under a density$
Module 3: Linear Algebra for Data Analytics
Lesson 3.1M3Vector and Matrix BasicsRunning case: Tartan Robotics, a warehouse robot fleet $Tartan Robotics: three warehouse robots, three readings each$ $A vector is an ordered list of features$ $The dot product turns a robot's readings and a manager's weights into one score$ $Matrix multiplication: the inner dimensions must match$ $Readiness scores for the whole fleet in one product, A·w$
Lesson 3.2M3Solving Linear Systems $How many Scouts, Haulers, and Lifters can Tartan build from the parts on hand?$ $The same system, repackaged as Ax = b$ $Gaussian elimination: three legal row moves$ $Unique, none, or infinitely many: three ways a linear system can end$ $Linear regression is a linear system in disguise: (XᵀX)β = Xᵀy$
Lesson 3.3M3Matrix Properties and Techniques $A task-weight matrix turns robot capabilities into task scores$ $The identity matrix: multiplying by I changes nothing$ $A 2×2 matrix has an inverse exactly when its determinant is not zero$ $Matrix algebra mostly follows the usual rules, except that AB ≠ BA$ $Working backward from target scores to capabilities with W⁻¹$
Lesson 3.4M3Eigenvalues and Eigenvectors $The defining equation: Av = λv$ $A stretch matrix tilts most vectors, but its eigenvectors only get longer$ $PCA in one sentence: the eigenvectors of the covariance matrix$ $Two components capture 83% of the variation across 400 robots$ $Where else eigen-thinking shows up: PageRank, eigenfaces, Markov chains$
Lesson 3.5M3Data Analytics Applications $Predicting each robot's daily throughput from its features$ $Every prediction is one dot product, so all of them together are ŷ = Xβ$ $The normal equations give the best-fitting β in closed form$ $Recommender systems and PageRank run on the same matrix primitives$ $Every Module 3 concept, mapped to where it lives in analytics$
Module 4: Descriptive Statistics and Data Visualization
Lesson 4.1M4Measures of Central TendencyRunning case: Steel City Streaming, a Pittsburgh sports streaming service $Steel City Streaming: what is a typical session when one viewer watched 395 minutes?$ $Three flavors of typical: mean, median, mode$ $Weighted averages: watch time by subscriber tier$ $Skewed data pulls the mean away from the median$ $Choosing the right measure, and what to watch out for with each$
Lesson 4.2M4Measures of Dispersion $Same average, different week: two broadcasts with very different spread$ $The range is easy to compute, but one outlier blows it up$ $Variance is the average squared distance from the mean$ $Same 45-minute mean, very different standard deviations$ $Variance is the language of risk in finance, operations, and analytics$
Lesson 4.3M4Data Distribution and Shape $From a list of 30 watch times to a histogram$ $Four classic shapes: bell, right-skewed, uniform, bimodal$ $The box plot: the five-number summary as a picture$ $Flagging outliers with the 1.5 × IQR rule$ $One 220-minute session moves the mean and SD but barely touches the median and IQR$
Lesson 4.4M4Correlation and Scatter Plots $The scatter plot: one point per week of marketing spend$ $Four classic patterns: positive, negative, none, nonlinear$ $What r of −0.9, −0.5, 0, 0.5, and 0.9 actually look like$ $What r will not tell you: causation, curves, outliers, effect size$ $Marketing spend and new subscribers: r = 0.80$
Lesson 4.5M4Principles of Data Visualization $Pick the chart that fits the question, never the other way around$ $Before the chart: who is the audience, what do they need to know, what should they do$ $No zero baseline, so 6 million enrollments look like a fraction of 7 million$ $The truncated y-axis trick in a newspaper chart of federal debt$ $Data should tell a story: ticket volume rebuilt around one ask$
Lesson 4.6M4Module 4 Hands-on PracticeIn-class exerciseFive exercises on one week of Steel City data $The dataset: peak concurrent viewers on eight Friday nights$ $Reading a histogram of 30 Friday nights$ $The five-number summary read off a box plot, with an outlier check$ $Correlation step by step, from deviations to r$ $The analyst's mini-report: the numbers turned into a short read for an executive$
Module 5: Probability Foundations and Random Variables
Lesson 5.1M5Probability ConceptsRunning case: Carnegie Quant Capital, a fictional Pittsburgh hedge fund $The vocabulary of probability, using one stock's daily move$ $Kolmogorov's three axioms: everything else is consequence$ $Disjoint or overlapping: can both events happen at once?$ $Why subtract the overlap: P(A) + P(B) counts the intersection twice$ $A decision tree for which probability rule you need$
Lesson 5.2M5Conditional Probability and Bayes' Theorem $Conditioning on B shrinks the world to B$ $A contingency table of 1,000 historical trading days$ $Bayes' theorem: posterior, likelihood, prior, evidence$ $A fraud alert that catches 99% of fraud is right only 9% of the time at a 0.5% base rate$ $The same fraud problem as a tree diagram$
Lesson 5.3M5Random Variables $A random variable is a function from outcomes to numbers$ $Three picks, eight outcomes, and X = 0, 1, 2, or 3 winners$ $Reading a PMF: the number of winning picks out of three$ $Reading a PDF: probability as area under the portfolio return curve$ $Two pictures, one idea: discrete probability lives in bars, continuous in area$
Lesson 5.4M5Key Discrete Distributions $Two questions: winners across ten picks, and compliance alerts per hour$ $Check BINS before you reach for the binomial$ $The shape of the binomial with n = 10 and p = 0.6$ $The Poisson distribution, where the mean and the variance are both λ$ $Bernoulli, binomial, or Poisson: which one to use$
Lesson 5.5M5Key Continuous Distributions $How likely is tomorrow to lose more than 2%?$ $Uniform, exponential, and normal: three shapes to recognize$ $The exponential distribution: waiting time between events$ $The 68-95-99.7 rule applied to daily ETF returns$ $A z-score turns a 2% loss into about 10 losing days a trading year$
Lesson 5.6M5Expectation and Variance $Is the strategy worth running? Payoff per trade is a random variable$ $Expected payoff: $0.70K per trade$ $What 0.70 means: never the outcome of one trade, always the long-run average$ $Same mean, very different risk$ $Variance rules a trading desk uses daily$
Module 6: Introduction to Statistical Inference
Lesson 6.1M6From Sample to PopulationRunning case: Three Rivers Health Analytics, ER wait times $Three Rivers Health: 220,000 ER visits, and a sample of 300$ $Why sample at all: cost, time, infeasibility, destruction$ $Sampling pitfalls, and the direction each one biases the estimate$ $The sample standard deviation, and why we divide by n − 1$ $Every random sample yields a slightly different x̄$
Lesson 6.2M6Sampling Distributions and the Central Limit Theorem $How spread out are the sample means across imaginary repeats?$ $Simulating 1,000 repeats of the ER study$ $The Central Limit Theorem as three claims and a bonus$ $Diminishing returns: to halve the standard error, quadruple the sample$ $How large is large enough depends on how skewed the population is$
Lesson 6.3M6Confidence Intervals $Point estimate versus interval estimate: 47 minutes, or 44.96 to 49.04$ $Critical z* values worth memorizing$ $With s and t instead of σ and z, the interval barely moves at n = 300$ $What 95% confident means: about 19 of 20 intervals cover the true mean$ $Watch the wording: the 95% describes the procedure, not μ$
Lesson 6.4M6Hypothesis Testing $Does Hospital A match the 50-minute national benchmark?$ $Courtroom logic: assume H₀ until the evidence is overwhelming$ $The test statistic counts how many standard errors the sample sits from H₀$ $Visualizing a two-sided p-value of 0.0455$ $Type I and Type II errors$

Method

How the course works

Each module ends where an analytics course picks up. Calculus ends with gradient descent and the sigmoid. Linear algebra ends with the normal equations, PCA, and PageRank. Probability works through a fraud alert that is 99% sensitive and still right only 9% of the time at a 0.5% base rate.

I wrote the scope and sequence with the MS in Business Analytics core faculty, working backward from what their courses need. Before recording, I checked every equation symbolically.

fig. 1 · Integration reverses differentiation

What students hand in

Major assignments

Pause-and-try problems

Every lesson stops at least once for a problem set in the running case, such as a new break-even point for the coffee shop or the standard error for a smaller hospital sample. Students pause, work it on paper, then watch the solution worked out by hand.

Module 4 hands-on practice

A full lesson of five exercises on one week of Steel City Streaming data: center, spread, a histogram, a box plot, and a correlation, ending with a one-paragraph analyst's report for an executive.

Diagnostic pretest, module quizzes, and posttest

The workshop is designed to open with a diagnostic pretest that shows each student which topics need the most work, give a short low-stakes quiz with immediate feedback at the end of each module, and close with a comprehensive posttest.

Revision history

How the course developed

A self-paced online course for incoming MS in Business Analytics students, built with Tepper's learning technologies team between December 2025 and August 2026. I recorded every lesson, about thirty short videos across six modules, each pairing slides with worked problems written out by hand.

Offerings

Summer 2026

Incoming MS in Business Analytics students take the workshop on Canvas.

All courses