This section contains a description of the courses I teach and associated material.
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"Never, ever, be afraid to ask for help: it is not a sign of weakness, but a sign of strength."
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
Philosophy of Education:
Students should reflect on the following questions (and their corresponding thoughts).
Why go to university?
To stimulate intellectual curiosity?
To develop practical skills?
Why learn mathematics?
To improve rational thinking?
To make other people think you are smart?
How should I approach any university course?
Find a connected topic/concept you are curious about learning (which may initially be difficult to understand) and try to understand how the course material is related to what you want to learn.
Why should I take this specific course (i.e. introductory statistics, general physics, linear algebra)?
Refer to the previous points and decide for yourself.
Personal Statement on Teaching
I am originally from Vancouver, Canada. I finished my Bachelor's degree in Finance in 3 years at the University of Calgary while also competing for their Track and Field team. Having 2 more years of athletic scholarship eligibility for which I wanted to complete a degree in mathematics, I reached out to schools across America. I ended up at Dominican College, a school I had never heard of having lived my entire life on the other side of the continent.
Transitioning from a large public research university of 30,000 students to a small private liberal arts college of 2,000 students was quite a change. However, I immediately noticed the pleasant benefits of such an intimate setting. Each of my professors knew who I was, what my interests were, and what my strengths and weaknesses as a student were. Opposed to a large research university, the primary job of each of my professors at Dominican was to ensure the success of their students. This change impacted me quite heavily: my professors were the ones who pushed me to pursue a graduate degree in mathematics, help me find part-time employment at the college while I was a student, and write glowing letters of recommendation for me for future job applications.
This influence was so impactful that it made me realize the beauty of the teaching discipline. The charisma of my professors swayed me to work as a teacher and instructor in mathematics immediately after graduating from Dominican in 2018. The guidance of my professors helped me receive a full scholarship to every PhD program in Mathematics I applied to that following winter.
I attended Virginia Tech on a graduate teaching assistantship in their mathematics program. After completing my Master of Science degree throughout the COVID pandemic, missing out on the in-person teaching opportunities that were normally a part of my graduate assistantship left me with an unfulfilled desire. Given an incredible opportunity, I then decided to teach full-time at Dominican for a year. Expecting to return for my PhD at Virginia Tech, it turned out that the community and opportunities at Dominican were too much to resist.
Today, I am the assistant professor of mathematics and physics at Dominican University. Every day, I walk up the same stairs to my office on the 3rd floor of the Prusmack Center – the place where I used to study endlessly to pass my classes and connect with my professors. I think about how my life changed as a result of this experience walking up those stairs, and I can't help but feel excited, grateful and blessed to try to pass on the joy I found at this institution to my current students.
It is my mission at Dominican University to help each of my students realize their true potential and break through self-imposed barriers the same way I did. It is my pride to show them it is possible.
Learning Resources for Mathematics:
For foundational topics (up to undergraduate mathematics), Khan Academy and OpenStax
For advanced topics (up to graduate mathematics), Open Math Notes, RealNotComplex, Class Central and Open Culture
How to Successfully Learn Mathematics:
The main ingredients determining one's success in anything they do: Curiosity, Confidence, Patience and Effort.
a. Mathematical proficiency has five strands (source):
Understanding: Comprehending mathematical concepts, operations, and relations—knowing what mathematical symbols, diagrams, and procedures mean.
Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently, and appropriately.
Applying: Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately.
Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.
Engaging: Seeing mathematics as sensible, useful, and doable—if you work at it—and being willing to do the work.
A simple way to carry out these five tasks in a university course:
(I) Reading the textbook, (II) Working through examples, (III) Struggling through practice problems, (IV) Discussing difficulties with professors and other students, (V) Understanding and building on what was accomplished, and (VI) Repeating this process consistently.
b. For each of the steps listed above, consider the method of René Descartes:
Never accept anything as true unless it is clearly known to be such.
Divide difficult problems into as many parts as possible.
Proceed from the simplest problems to the more complex.
Make the connection complete and general so that nothing has been overlooked.
Benefits of Mathematical Reasoning:
Improved Problem Identification (Identifying which path to take, i.e. asking the right questions)
Improved Analytical/Logical Reasoning (Proceeding along a path, i.e. using problem-solving methods)
Improved Solution Justification (Recognizing when the end of a path is reached, i.e. providing robust and stable solutions)