Dominican Curriculum 47X: Capstone Research Project

Syllabus

(This is a general education curriculum capstone course which all students at Dominican are required to take.) 

Students will produce a reflective e-portfolio, annotated bibliographies, a persuasive white paper written in such a way that the problem and response are articulated using a multidisciplinary framework, and a classroom lesson to be taught as an interactive case study that also explores how a response might impact diverse peoples and groups. In producing these things, students “close the loop” by which they envision a world in which we take responsibility for these risks and develop and evaluate concrete proposals for doing so. 

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

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 an 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. 

Dominican University Policy Manual, Volume IV (Faculty Personnel Policies)

Section 4.1.2.5: Advancement in Rank to Assistant Professor  

To advance to the rank of Assistant Professor an individual must (i) hold a minimum of master's degree in the individual’s teaching discipline from a regionally accredited or internationally recognized institution of higher education and have made substantive progress toward obtaining a doctorate or its equivalent in an appropriate field or discipline or (ii) hold multiple Master's degrees from a regionally accredited or internationally recognized institution of higher education that serve the needs of the University or hold a master's degree from a regionally accredited or internationally recognized institution of higher education and substantial professional, artistic, or other relevant experience.

In addition, the person must have had a minimum of three years of successful teaching in higher education or a combination of successful teaching and professional experience relevant to the field  of appointment.

Application for advancement to this rank may be submitted after completion of two years of full-time service at Dominican University by those who have fulfilled the minimum requirement of three years of successful full-time teaching in higher education.

Applicants are further required to have satisfactorily met the criteria for faculty performance set forth in Section 4.6 - Evaluation.  

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.

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):

1. Understanding: Comprehending mathematical concepts, operations, and relations—knowing what mathematical symbols, diagrams, and procedures mean.

2. Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently, and appropriately.

3. Applying: Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately.

4. Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.

5. 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: 

1. Never accept anything as true unless it is clearly known to be such.

2. Divide difficult problems into as many parts as possible.

3. Proceed from the simplest problems to the more complex.

4. Make the connection complete and general so that nothing has been overlooked.

Benefits of Mathematical Reasoning:

1. Improved Problem Identification (Identifying which path to take, i.e. asking the right questions)

2. Improved Analytical/Logical Reasoning (Proceeding along a path, i.e. using problem-solving methods)

3. Improved Solution Justification (Recognizing when the end of a path is reached, i.e. providing robust and stable solutions)