Math 334: Advanced Calculus

Syllabus

Textbook: W. Kosmala, A Friendly Introduction to Analysis: Single and Multivariable (2nd Ed.), 2004

Foundations of Analysis and proof. Limits, topology, sequences, series, continuity and differentiation from a theoretical perspective.

1. Introduction

2. Sequences

3. Limits of Functions

4. Continuity

5. Differentiation

6. Integration

7. Infinite Series

8. Sequences and Series of Functions

Math 332: Linear Algebra

Syllabus

Textbook: Williams, G., Linear Algebra with Applications (9th Ed.), 2019

Matrices and their operations; determinants; linear equations and linear dependence; vector spaces and linear transformations. 

1. Linear Equations and Vectors

1.1 Matrices and Systems of Linear Equations

1.2 Gauss-Jordan Elimination

1.3 The Vector Space "R^n"

1.4 Subspaces of R^n

1.5 Basis and Dimension

1.6 Dot Product, Norm, Angle, and Distance

2. Matrices and Linear Transformations

2.1 Addition, Scalar Multiplication, and Multiplication of Matrices

2.2 Properties of Matrix Operations

2.3 Symmetric Matrices

2.4 Inverse of a Matrix

2.5 Matrix Transformations, Rotations, and Dilations

2.6 Linear Transformations

3. Determinants and Eigenvectors

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Determinants, Matrix Inverses, and Systems of Linear Equations

3.4 Eigenvalues and Eigenvectors

4. General Vector Spaces

4.1 General Vector Spaces and Subspaces

4.2 Linear Combinations of Vectors

4.3 Linear Independence of Vectors

4.4 Properties of Bases

4.5 Rank

Math 222: Calculus II

Syllabus

Textbook: Larson, Roland E., Edwards, Bruce H.: Calculus (12th Ed.), Cengage publishing, 2019

Integrals; the definite integral; exponential, logarithmic and trigonometric functions; formal methods of integration; basic properties of continuous and differentiable functions; area and volume.

1. Integration (Text Ch 4)

1. Antiderivatives (Text 4.1)

2. Area (Text 4.2, 4.3)

3. Fundamental Theorem of Calculus (Text 4.4)

4. Integration by Substitution (Text 4.5)

2. Special Functions (Text Ch 5)

1. The Natural Logarithmic Function (Text 5.1, 5.2)

2. Inverse Functions (Text 5.3)

3. Exponential Functions (Text 5.4, 5.5)

4. Indeterminate Forms (Text 5.6)

5. Inverse Trigonometric Functions (Text 5.7, 5.8)

3. Differential Equations (Text Ch 6)

1. Euler's Method (Text 6.1)

2. Growth and Decay (Text 6.2)

3. Separation of Variables (Text 6.3)

4. Applications of Integration (Text Ch 7)

1. Area of a Region (Text 7.1)

2. Volume of a Region (Text 7.2, 7.3)

3. Arc Length (Text 7.4)

5. Integration Techniques (Text Ch 8)

1. Integration by Parts (Text 8.2)

2. Trigonometric Functions (Text 8.3, 8.4)

3. Partial Fraction Decomposition (Text 8.5)

4. Numerical Integration (Text 8.6)

Physics 222: General Physics II

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of waves, optics, electricity, and magnetism.

1. Oscillations

2. Sound

3. Superposition

4. Wave Optics

5. Ray Optics

6. Optical Instruments

7. Electric Fields

8. Electric Potential

9. Current and Resistance

10. Circuits

11. Magnetic Fields

12. Induction

13. AC Electricity

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 221: Calculus I

Syllabus

Textbook: Larson, Roland E., Edwards, Bruce H.: Calculus (12th Ed.), Cengage publishing, 2019

Analytic geometry and functions; limits and continuity; derivatives, and applications of derivatives.

0. Preparation for Calculus (Text Ch P)

0.1. Graphs, Models, Rates of Change (Text P.1, P.2)

0.2. Functions and Graphs (Text P.3, P.4)

1. Limits and Their Properties (Text Ch 1)

1.1. Preview of Calculus (Text 1.1)

1.2. Finding Limits (Text 1.2)

1.3. Evaluating Limits (Text 1.3)

1.4. Continuity and One-Sided Limits (Text 1.4)

1.5. Infinite Limits (Text 1.5)

2. Differentiation (Text Ch 2)

2.1. The Derivative (Text 2.1)

2.2. Differentiation Rules (Text 2.2)

2.3. Higher-Order Derivatives (Text 2.3)

2.4. The Chain Rule (Text 2.4)

2.5. Implicit Differentiation (Text 2.5)

2.6. Related Rates (Text 2.6)

3. Applications of Differentiation (Text Ch 3)

3.1. Extrema in an Interval (Text 3.1)

3.2. Rolle’s Theorem and the Mean Value Theorem (Text 3.2)

3.3. Increasing/Decreasing Functions (Text 3.3)

3.4. Concavity (Text 3.4)

3.5. Limits at Infinity (Text 3.5)

3.6. Curve Sketching (Text 3.6)

3.7. Optimization Problems (Text 3.7)

3.8. Newton’s Method (Text 3.8)

Physics 221: General Physics I

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of force, motion, conservation laws, and properties of matter.

1. Force and Motion

1.1. Representing Motion

1.2. Motion in One Dimension

1.3. Vectors and Motion in Two Dimensions

1.4. Forces and Newton's Laws of Motion

1.5. Applying Newton's Laws

1.6. Circular Motion, Orbits, and Gravity

1.7. Rotational Motion

1.8. Equilibrium and Elasticity

2. Conservation Laws

2.1. Momentum

2.2. Energy and Work

2.3. Using Energy

3. Properties of Matter

3.1. Thermal Properties of Matter

3.2. Fluids

Physics 203: Patterns in Nature

Syllabus

Textbook: McKirahan, Richard D. Philosophy before Socrates: An Introduction with Texts and Commentary. Hackett, 2011.

A study of the pre-Socratic intellectual revolution that contributed to the development of foundational ideas of modern scientific disciplines, such as biology, chemistry, mathematics and physics. Topics covered include early ideas of cosmology, geometry, atoms, and medicine.

1. Introduction and Hesiod

2. Milesians (Thales, Anaximander, Anaximenes) and Xenophanes

3. Pythagoras and Heraclitus

4. Eleatics (Parmenides, Zeno, Melissus) and Pluralists (Anaxagoras, Empedocles)

5. Atomists (Leuccipus, Democritus)

6. Diogenes of Apollonia and Philolaus of Croton

7. Sophists (Protagoras, Giorgas, Hippias, et al.)

8. Convention vs. Nature and Early Medicine (Hippocrates)

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Physics 222: General Physics II

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of waves, optics, electricity, and magnetism.

1. Oscillations

2. Sound

3. Superposition

4. Wave Optics

5. Ray Optics

6. Optical Instruments

7. Electric Fields

8. Electric Potential

9. Current and Resistance

10. Circuits

11. Magnetic Fields

12. Induction

13. AC Electricity

Link to Python Files

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 113: College Algebra

Syllabus

Polynomials and factoring; linear and quadratic equations; functions and graphs.  

1. Basic Concepts

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Powers, Square Roots, and the Order of Operations

1.4 Integer Exponents and Scientific Notation

1.5 Operations with Variables and Grouping Symbols

1.6 Evaluating Variable Expressions and Formulas

2. Linear Equations and Inequalities

2.1 First-Degree Equations with One Unknown

2.2 Literal Equations and Formulas

2.3 Absolute Value Equations

2.4 Using Equations to Solve Word Problems

2.5 Solving More-Involved Word Problems

2.6 Linear Inequalities

2.7 Compound Inequalities

2.8 Absolute Value Inequalities

3. Equations and Inequalities in Two Variables and Functions

3.1 Graphing Linear Equations with Two Unknowns

3.2 Slope of a Line

3.3 Graphs and the Equations of a Line

4. Systems of Linear Equations and Inequalities

4.1 Systems of Linear Equations in Two Variables

4.3 Applications of Systems of Linear Equations

5. Polynomials

5.1 Introduction to Polynomials and Polynomial Functions: Adding, Subtracting, and Multiplying

5.2 Dividing Polynomials

5.4 Removing Common Factors; Factoring by Grouping

5.5 Factoring Trinomials

5.6 Special Cases of Factoring

5.7 Factoring a Polynomial Completely

5.8 Solving Equations and Applications Using Polynomials

6. Rational Expressions and Equations

6.1 Rational Expressions and Functions: Simplifying, Multiplying, and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Rational Expressions

6.4 Rational Equations

7. Rational Exponents and Radicals

7.1 Rational Exponents

7.2 Radical Expressions and Functions

7.3 Simplifying, Adding, and Subtracting Radicals

7.4 Multiplying and Dividing Radicals

7.5 Radical Equations

7.6 Complex Numbers

8. Quadratic Equations and Inequalities

8.1 Quadratic Equations

8.2 The Quadratic Formula and Solutions to Quadratic Equations

8.3 Equations That Can Be Transformed into Quadratic Form

8.4 Formulas and Applications

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 335: Differential Equations

Syllabus

Textbook: Edwards, C. H. and Penney, D. E., Elementary Differential Equations (6th edition), 2007

Solutions of first order equations; modeling applications; equations of higher order; series solutions; Laplace transforms.

1. First-Order Differential Equations

2. Linear Equations of Higher Order

3. Power Series

4. Laplace Transforms

5. First-Order Systems and Applications

Math 332: Linear Algebra

Syllabus

Textbook: Williams, G., Linear Algebra with Applications (9th Ed.), 2019

Matrices and their operations; determinants; linear equations and linear dependence; vector spaces and linear transformations. 

1. Linear Equations and Vectors

1.1 Matrices and Systems of Linear Equations

1.2 Gauss-Jordan Elimination

1.3 The Vector Space "R^n"

1.4 Subspaces of R^n

1.5 Basis and Dimension

1.6 Dot Product, Norm, Angle, and Distance

2. Matrices and Linear Transformations

2.1 Addition, Scalar Multiplication, and Multiplication of Matrices

2.2 Properties of Matrix Operations

2.3 Symmetric Matrices

2.4 Inverse of a Matrix

2.5 Matrix Transformations, Rotations, and Dilations

2.6 Linear Transformations

3. Determinants and Eigenvectors

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Determinants, Matrix Inverses, and Systems of Linear Equations

3.4 Eigenvalues and Eigenvectors

4. General Vector Spaces

4.1 General Vector Spaces and Subspaces

4.2 Linear Combinations of Vectors

4.3 Linear Independence of Vectors

4.4 Properties of Bases

4.5 Rank

Physics 221: General Physics I

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of force, motion, conservation laws, and properties of matter.

1. Force and Motion

1.1. Representing Motion

1.2. Motion in One Dimension

1.3. Vectors and Motion in Two Dimensions

1.4. Forces and Newton's Laws of Motion

1.5. Applying Newton's Laws

1.6. Circular Motion, Orbits, and Gravity

1.7. Rotational Motion

1.8. Equilibrium and Elasticity

2. Conservation Laws

2.1. Momentum

2.2. Energy and Work

2.3. Using Energy

3. Properties of Matter

3.1. Thermal Properties of Matter

3.2. Fluids

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 336: Numerical Analysis

Syllabus

Textbook: E. Sullivan, Numerical Methods: An Inquiry-Based Approach With Python, 2022.

Mathematical analysis of interpolation procedures, polynomial approximation, numerical differentiation and integration. Also includes methods for solving equations, solutions of ordinary differential equations, approximations of least squares, and curve fitting.

1. Preliminary Topics

2. Algebra

3. Calculus

4. Linear Algebra

5. Ordinary Differential Equations

6. Partial Differential Equations

Math 334: Advanced Calculus

Syllabus

Textbook: W. Kosmala, A Friendly Introduction to Analysis: Single and Multivariable (2nd Ed.), 2004

Foundations of Analysis and proof. Limits, topology, sequences, series, continuity and differentiation from a theoretical perspective.

1. Introduction

2. Sequences

3. Limits of Functions

4. Continuity

5. Differentiation

6. Integration

7. Infinite Series

8. Sequences and Series of Functions

Physics 222: General Physics II

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of waves, optics, electricity, and magnetism.

1. Oscillations

2. Sound

3. Superposition

4. Wave Optics

5. Ray Optics

6. Optical Instruments

7. Electric Fields

8. Electric Potential

9. Current and Resistance

10. Circuits

11. Magnetic Fields

12. Induction

13. AC Electricity

Link to Python Files

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Physics 221: General Physics I

Syllabus

Textbook: Knight, Jones, Field, College Physics: a strategic approach (4th Ed.), 2019

An algebra-based approach to the basic concepts of force, motion, conservation laws, and properties of matter.

1. Force and Motion

1.1. Representing Motion

1.2. Motion in One Dimension

1.3. Vectors and Motion in Two Dimensions

1.4. Forces and Newton's Laws of Motion

1.5. Applying Newton's Laws

1.6. Circular Motion, Orbits, and Gravity

1.7. Rotational Motion

1.8. Equilibrium and Elasticity

2. Conservation Laws

2.1. Momentum

2.2. Energy and Work

2.3. Using Energy

3. Properties of Matter

3.1. Thermal Properties of Matter

3.2. Fluids

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

Math 331: Abstract Algebra

Syllabus

Textbook: Fraleigh, J. and Brand, N., A First Course in Abstract Algebra (8th Ed.), 2021

Groups, subgroups, rings, integral domains and fields. 

1. Groups

1.1 Sets and Relations

1.2 Binary Operations

1.3 Groups

1.4 Abelian Groups

1.5 Nonabelian Groups

2. Homomorphisms

2.1 Subgroups

2.2 Factor Groups

2.3 Normal Subgroups

3. Rings

3.1 Rings and Fields

3.2 Divisibility and Integral Domains

3.3 Euler's Theorem

3.4 Cryptography

Information Technology 240: Programming I

Syllabus

Textbook: Gaddis, T., Starting Out with Python (4th Ed.), 2018

Software development environment, functions, variables, IF statements, forms, input/output, loops, structures and class objects. 

1. Introduction to Computers and Programming

2. Input, Processing and Output

3. Decision Structures and Boolean Logic

4. Repetition Structures

5. Functions

6. Sequences

7. Strings

8. Files and Data

9. Collections and Serialization

10. Introduction to Objects and Classes

Information Technology 200: Computer-Based Systems

Syllabus

Textbook: Andrews, J., Dark, J. and West, J., CompTIA A+ Guide to IT Technical Support (10th Ed.), 2020

PC technology, internet technology, operating systems, applications, I/O, USB, video systems and computer viruses. 

1. Physical Systems

1.1 Hardware

• Cables

• Connectors

• RAM

• Storage

• Motherboards and CPUs

• Peripheral Devices

• Power Supply

1.2 Mobile Devices

• Laptop Hardware

• Laptop Components

• Laptop Features

• Other Mobile Devices

1.3 Networking

• TCP and UDP

• Networking Hardware

• Wireless Protocols

• Network Servers

• Network Configuration

• Network Connection

1.4 Virtualization

• Cloud Computing

2. Virtual Systems

2.1 Operating Systems

• System Types

• Windows

• Windows Command-Line

• Windows Control Panel

• Windows Applications

• Macintosh

• Linux

2.2 Security

• Physical Security

• Security Concepts

• Security Protocal

• Malware Tools

• Social Engineering

Math 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

Math 113: College Algebra

Syllabus

Textbook: Tobey, J. et al., Intermediate Algebra (8th Ed.), 2017

Polynomials and factoring; linear and quadratic equations; functions and graphs.  

1. Basic Concepts

1.1 The Real Number System

1.2 Operations with Real Numbers

1.3 Powers, Square Roots, and the Order of Operations

1.4 Integer Exponents and Scientific Notation

1.5 Operations with Variables and Grouping Symbols

1.6 Evaluating Variable Expressions and Formulas

2. Linear Equations and Inequalities

2.1 First-Degree Equations with One Unknown

2.2 Literal Equations and Formulas

2.3 Absolute Value Equations

2.4 Using Equations to Solve Word Problems

2.5 Solving More-Involved Word Problems

2.6 Linear Inequalities

2.7 Compound Inequalities

2.8 Absolute Value Inequalities

3. Equations and Inequalities in Two Variables and Functions

3.1 Graphing Linear Equations with Two Unknowns

3.2 Slope of a Line

3.3 Graphs and the Equations of a Line

4. Systems of Linear Equations and Inequalities

4.1 Systems of Linear Equations in Two Variables

4.3 Applications of Systems of Linear Equations

5. Polynomials

5.1 Introduction to Polynomials and Polynomial Functions: Adding, Subtracting, and Multiplying

5.2 Dividing Polynomials

5.4 Removing Common Factors; Factoring by Grouping

5.5 Factoring Trinomials

5.6 Special Cases of Factoring

5.7 Factoring a Polynomial Completely

5.8 Solving Equations and Applications Using Polynomials

6. Rational Expressions and Equations

6.1 Rational Expressions and Functions: Simplifying, Multiplying, and Dividing

6.2 Adding and Subtracting Rational Expressions

6.3 Complex Rational Expressions

6.4 Rational Equations

7. Rational Exponents and Radicals

7.1 Rational Exponents

7.2 Radical Expressions and Functions

7.3 Simplifying, Adding, and Subtracting Radicals

7.4 Multiplying and Dividing Radicals

7.5 Radical Equations

7.6 Complex Numbers

8. Quadratic Equations and Inequalities

8.1 Quadratic Equations

8.2 The Quadratic Formula and Solutions to Quadratic Equations

8.3 Equations That Can Be Transformed into Quadratic Form

8.4 Formulas and Applications

MA 225: Introduction to Statistics

Syllabus

Textbook: Bluman, A., Elementary Statistics: A Brief Version (8th Ed.), 2019

The nature and scope of statistical inquiries; collection and presentation of data; descriptive methods with particular reference to frequency distribution analysis; central tendency and dispersion; the normal curve; statistical inference and sampling methods; t-tests and p-value.

1. The Nature and Probability of Statistics

2. Frequency Distributions and Graphs

3. Data Description

4. The Normal Distribution

5. Confidence Intervals and Sample Size

6. Hypothesis Testing

7. Probability and Counting Rules

MA 332: Linear Algebra

Syllabus

Textbook: Williams, G., Linear Algebra with Applications (9th Ed.), 2019

Matrices and their operations; determinants; linear equations and linear dependence; vector spaces and linear transformations. 

1. Linear Equations and Vectors

1.1 Matrices and Systems of Linear Equations

1.2 Gauss-Jordan Elimination

1.3 The Vector Space "R^n"

1.4 Subspaces of R^n

1.5 Basis and Dimension

1.6 Dot Product, Norm, Angle, and Distance

2. Matrices and Linear Transformations

2.1 Addition, Scalar Multiplication, and Multiplication of Matrices

2.2 Properties of Matrix Operations

2.3 Symmetric Matrices

2.4 Inverse of a Matrix

2.5 Matrix Transformations, Rotations, and Dilations

2.6 Linear Transformations

3. Determinants and Eigenvectors

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Determinants, Matrix Inverses, and Systems of Linear Equations

3.4 Eigenvalues and Eigenvectors

4. General Vector Spaces

4.1 General Vector Spaces and Subspaces

4.2 Linear Combinations of Vectors

4.3 Linear Independence of Vectors

4.4 Properties of Bases

4.5 Rank

MA 116: Finite Mathematics

Syllabus

Textbook: Rolf, H., Finite Mathematics (8th Ed.), 2014

Linear equations and inequalities; matrix algebra and linear programming; the mathematics of finance. 

1. Functions and Lines

1.1 Functions

1.2 Graphs and Lines

1.3 Linear Models

2. Linear Systems

2.1 Systems of Two Equations

2.2 Matrix Representation

2.3 Gauss-Jordan Elimination

2.4 Matrix Operations

2.5 Matrix Multiplication

2.6 Matrix Inverses

3. Linear Programming

3.2 Systems of Linear Inequalities

3.3 Optimization Problems

4. Simplex Method

4.1 Introduction

4.2 Standard Maximum Problems

4.3 Standard Minimum Problems

4.4 Standard Problems with General Constraints

5. Mathematics of Finance

5.1 Simple Interest

5.2 Compound Interest

5.3 Regular Annuities

5.4 Amortized Annuities

MA 113: College Algebra

Syllabus

Textbook: Tobey, J. et al., Intermediate Algebra (8th Ed.), 2017

Polynomials and factoring; linear and quadratic equations; functions and graphs.  

1. Basic Concepts

2. Linear Equations and Inequalities

3. Equations and Inequalities in Two Variables and Functions

4. Systems of Linear Equations and Inequalities

5. Polynomials

6. Rational Expressions and Equations

7. Rational Exponents and Radicals

8. Quadratic Equations and Inequalities

CMDA 2006: Integrated Quantitative Science (Teaching Assistant)

[Additional Notes: Salt Mixing Initial Value Problem]

Recommended Textbooks: 

1. Elementary Differential Equations with Boundary Value Problems, by Kohler and Johnson, 2nd Edition

2a. Linear Algebra: A Modern Introduction, by Poole, 4th edition; or

2b. Linear Algebra and Its Applications, by Lay, 4th edition.

We will cover fundamental topics in linear algebra and differential equations. We shall concentrate on essential techniques for understanding and manipulating matrices and build understanding of system modeling through differential equations. These topics are the foundation of modern research and industrial practice in computational and data science. Specific topics include: 

1. Orthogonality, and orthogonal decompositions 

2. Matrix factorizations, and Computational Solution of Linear Systems 

3. Eigenvalues, diagonalization, singular value decomposition, Computation of Eigenvalues 

4. Ordinary differential equations, first and second order 

5. Systems of differential equations, nonlinear systems 

6. Numerical methods of solving systems of ODEs (with Python) 

MATH 1454: Introduction to Mathematical Problem-Solving (Teaching Assistant)

Textbook: Insight Through Computing: A MATLAB Introduction to Computational Science and Engineering, by Van Loan and Fan, 2010 

This course provides an introduction to mathematical problem-solving strategies and implementation through computer programming. The focus is on using a computer to solve some prototypical mathematical problems with basic programming skills that involve topics such as an introduction to logic (Boolean expressions and conditional statements), iterative processes and recursion, adaptive algorithms, Monte Carlo integration and random walks, visualization and presentation of mathematical objects, computational geometry, graph theory applications and representation. This course also prepares incoming freshman to have basic programming skills needed for the degree in Mathematics early on in their academic career. 

Math 1226: Integral Calculus (Teaching Assistant)

Textbook: Stewart, J., Calculus: Early Transcendentals (8th Ed.), 2016

[Additional Notes: Proof of The Natural Exponential Function]

Review:

• Indeterminate Forms and L'Hôpital's Rule

• The Definite Integral

• The Substitution Rule

Applications of Integration:

• Areas Between Curves

• Volumes by Disks/Washers

• Volumes by Cylindrical Shells

• Work

• Average Value of a Function

Techniques of Integration:

• Integration by Parts

• Trigonometric Integrals

• Trigonometric Substitution

• Integration of Rational Functions by Partial Fractions

• Approximate Integration

Further Applications of Integration:

• Economics (Gini Index)

• Physics and Engineering (Centers of Mass)

• Probability

Infinite Sequences and Series

• Convergence and Divergence

• Tests for Convergence

• Power Series

• Taylor and Maclaurin Series

• Applications of Taylor Polynomials

Math 1524: Business Calculus (Lab Instructor)

Each Lab is completed using Microsoft Excel. A summary of what topics are covered in each lab:

Lab 1: Introduction to Excel

Lab 2: Functions and Operations in Excel

Lab 3: Income Inflation - Introduction to Scatter Plots and PRODUCT function 

Lab 4: Consumer Demand - Introduction to Linear Regression and CORREL function

Lab 5: Time Value of Money and Mortgages

Lab 6: Revenue Forecasting - Introduction to SUM function

Lab 7: Growth Rates and Financial Statement Analysis - Introduction to AVERAGE function

Lab 8: Budgeting in Hospitality Industry

Lab 9: Economic Order Quantity and Inventory Management

Lab 10: Revenue Maximization and Break-Even Analysis