Spring 2025 - Dominican University
Math 334: Advanced Calculus
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
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
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
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
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
Winter 2024 - Dominican University
Math 225: Introduction to Statistics
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
Fall 2024 - Dominican University
Math 221: Calculus I
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
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
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
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
Summer 2024 - Dominican University
Math 225: Introduction to Statistics
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
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
Spring 2024 - Dominican University
Physics 222: General Physics II
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
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
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
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
Winter 2024 - Dominican University
Math 225: Introduction to Statistics
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
Fall 2023 - Dominican University
Math 335: Differential Equations
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
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
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
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
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
Summer 2023 - Dominican University
Math 225: Introduction to Statistics
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
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
Spring 2023 - Dominican University
Math 336: Numerical Analysis
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
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
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
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
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
Fall 2022 - Dominican University
Physics 221: General Physics I
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
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
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
Summer 2022 - Dominican University
Math 225: Introduction to Statistics
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
Spring 2022 - Dominican College
Math 331: Abstract Algebra
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
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
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
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
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
Winter 2022 - Dominican College
MA 225: Introduction to Statistics
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
Fall 2021 - Dominican College
MA 332: Linear Algebra
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
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
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
Fall 2020 - Virginia Tech
CMDA 2006: Integrated Quantitative Science (Teaching Assistant)
[Additional Notes: Salt Mixing Initial Value Problem]
Recommended Textbooks:
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.
Summer 2020 - Virginia Tech
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
Fall 2019 & Spring 2020 - Virginia Tech
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