Our online classes are regular Michigan Tech classes available to anyone qualified to take classes at Tech, anywhere in the world. Students earn course credit, the same as any on-campus class. Students must meet the standard prerequisites for each course.

## Summer 2021

## MA 2160 - Calculus with Technology II

Continued study of calculus, which includes a computer laboratory. Topics include integration and its uses, function approximation, vectors, and elementary modeling with differential equations.

**Credits:**4.0**Lec-Rec-Lab:**(0-3-1)**Semesters Offered:**Fall, Spring, Summer**Pre-Requisite(s):**MA 1160 or MA 1161 or MA 1135 or MA 1121 or CEEB Calculus AB >= 3 or CEEB Calculus BC >= 3 or CEEB Calculus AB Subscore >= 3

## MA 2320 - Elementary Linear Algebra

An introduction to linear algebra and how it can be used. Topics include systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Software Engineering, Computer Science**Pre-Requisite(s):**MA 1160 or MA 1161 or MA 1135 or MA 1121

## MA 3160 - Multivariable Calculus with Technology

Introduction to calculus in two and three dimensions, which includes a computer laboratory. Topics include functions of several variables, partial derivatives, the gradient, multiple integrals; introduction to vector-valued functions and vector calculus, divergence, curl, and the integration theorems of Green, Stokes, and Gauss.

**Credits:**4.0**Lec-Rec-Lab:**(0-3-1)**Semesters Offered:**Fall, Spring, Summer**Pre-Requisite(s):**MA 2160 or CEEB Calculus BC >= 3

## MA 3520 - Elementary Differential Equations

First order equations, linear equations, and systems of equations.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Computer Science**Pre-Requisite(s):**MA 2160 and (MA 2320 or MA 2321 or MA 2330)

## MA 3710 - Engineering Statistics

Introduction to the design, conduct, and analysis of statistical studies aimed at solving engineering problems. Topics include methods of data collection, descriptive and graphical methods, probability and probability models, statistical inference, control charts, linear regression, design of experiments.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Pre-Requisite(s):**MA 2160

## MA 4515 - Introduction to Partial Differential Equations

An introduction to solution techniques for linear partial differential equations. Topics include: separation of variables, eigenvalue and boundary value problems, spectral methods, fourier series, and Green's functions. Studies applications in heat and mass transfer (diffusion eqn.), and mechanical vibrations (wave and beam eqns.).

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Spring, Summer**Pre-Requisite(s):**(MA 3520 or MA 3521 or MA 3530 or MA 3560) and MA 3160

### Open to Keypath Students Only

## MA 4700 - Probability and Statistical Inference I

Introduction to probabilistic methods. Topics include probability laws, counting rules, discrete and continuous random variables, moment generating functions, expectation, joint distributions, and the Central Unit Theorem.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Permission of department required**Pre-Requisite(s):**MA 3160 and (MA 2710 or MA 2720 or MA 3710 or MA 3715)

## MA 5701 - Statistical Methods

Introduction to design, conduct, and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics include design, descriptive, and graphical methods, probability models, parameter estimation and hypothesis testing.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Must be enrolled in one of the following Level(s): Graduate

## Fall 2020

## MA 2320 - Elementary Linear Algebra

An introduction to linear algebra and how it can be used. Topics include systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Software Engineering, Computer Science**Pre-Requisite(s):**MA 1160 or MA 1161 or MA 1135 or MA 1121

## MA 3520 - Elementary Differential Equations

First order equations, linear equations, and systems of equations.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Computer Science**Pre-Requisite(s):**MA 2160 and (MA 2320 or MA 2321 or MA 2330)

## MA 3710 - Engineering Statistics

Introduction to the design, conduct, and analysis of statistical studies aimed at solving engineering problems. Topics include methods of data collection, descriptive and graphical methods, probability and probability models, statistical inference, control charts, linear regression, design of experiments.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Pre-Requisite(s):**MA 2160

### Open to Keypath Students Only

## MA 4700 - Probability and Statistical Inference I

Introduction to probabilistic methods. Topics include probability laws, counting rules, discrete and continuous random variables, moment generating functions, expectation, joint distributions, and the Central Unit Theorem.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Permission of department required**Pre-Requisite(s):**MA 3160 and (MA 2710 or MA 2720 or MA 3710 or MA 3715)

## MA 5701 - Statistical Methods

Introduction to design, conduct, and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics include design, descriptive, and graphical methods, probability models, parameter estimation and hypothesis testing.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Must be enrolled in one of the following Level(s): Graduate

## MA 5761 - Computational Statistics

Introduction to computationally intensive statistical methods. Topics include resampling methods, Monte Carlo simulation methods, smoothing technique to estimate functions, and methods to explore data structure. This course will use the statistical software R.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall**Pre-Requisite(s):**MA 4770(C) or (MA 4700 and MA 5701)

## MA 5781 - Time Series Analysis and Forecasting

Statistical modeling and inference for analyzing experimental data that have been observed at different points in time. Topics include models for stationary and non stationary time series, model specification, parametric estimation, model diagnostics and forecasting, seasonal models and time series regression models.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Spring**Pre-Requisite(s):**(MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701) and (MA 3720 or EE 3180 or MA 4700)

## Spring 2021

## MA 2320 - Elementary Linear Algebra

An introduction to linear algebra and how it can be used. Topics include systems of equations, vectors, matrices, orthogonality, subspaces, and the eigenvalue problem.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Software Engineering, Computer Science**Pre-Requisite(s):**MA 1160 or MA 1161 or MA 1135 or MA 1121

## MA 3520 - Elementary Differential Equations

First order equations, linear equations, and systems of equations.

**Credits:**2.0**Lec-Rec-Lab:**(0-2-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**May not be enrolled in one of the following Major(s): Mathematics, Computer Science**Pre-Requisite(s):**MA 2160 and (MA 2320 or MA 2321 or MA 2330)

## MA 3710 - Engineering Statistics

Introduction to the design, conduct, and analysis of statistical studies aimed at solving engineering problems. Topics include methods of data collection, descriptive and graphical methods, probability and probability models, statistical inference, control charts, linear regression, design of experiments.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Pre-Requisite(s):**MA 2160

### Open to Keypath Students Only

## MA 4700 - Probability and Statistical Inference I

Introduction to probabilistic methods. Topics include probability laws, counting rules, discrete and continuous random variables, moment generating functions, expectation, joint distributions, and the Central Unit Theorem.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Permission of department required**Pre-Requisite(s):**MA 3160 and (MA 2710 or MA 2720 or MA 3710 or MA 3715)

## MA 4705 - Probability and Statistical Inference II

Topics include sampling distributions, theory of point and interval estimation, properties of estimators, and theory of hypothesis testing.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**On Demand**Restrictions:**Permission of department required**Pre-Requisite(s):**MA 4700

## MA 4720 - Design and Analysis of Experiments

Covers construction and analysis of completely randomized, randomized block, incomplete block, Latin squares, factorial, fractional factorial, nested and split-plot designs. Also examines fixed, random and mixed effects models and multiple comparisons and contrasts. The SAS statistical package is an integral part of the course.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Spring**Pre-Requisite(s):**MA 2710 or MA 2720 or MA 3710 or MA 3715 or MA 5701

## MA 5701 - Statistical Methods

Introduction to design, conduct, and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics include design, descriptive, and graphical methods, probability models, parameter estimation and hypothesis testing.

**Credits:**3.0**Lec-Rec-Lab:**(0-3-0)**Semesters Offered:**Fall, Spring, Summer**Restrictions:**Must be enrolled in one of the following Level(s): Graduate