MCNEESE STATE UNIVERSITY | SPRING 2026

Mathematical Methods for Chemistry

The Grammar of Reality

"I learned very early the difference between knowing the name of something and knowing something." — Richard Feynman

Instructor

Kiran Boggavarapu, Ph.D.

kiran@mcneese.edu

Office

Kirkman 224E

Phone

(337) 475-5768

Class Time

TR 9:00–10:15 AM

Location

Kirkman 202

Office Hours

MWF 8–9 AM, 10–11 AM | TR 10:30 AM–12 PM | or by appointment

Course Description

Mathematics is the language of chemistry. This course teaches you to see the mathematical patterns hidden in chemical phenomena—and to summon the right tools when you recognize them.

Traditional math courses say: "Here's a tool. Find applications." This course inverts the pedagogy: "See the phenomenon. Recognize the pattern. The tool follows."

You will learn to perceive reality through nine cognitive primitives—fundamental patterns that appear across all of chemistry. Once you recognize these patterns, the mathematics becomes obvious: it's just notation for what you already see.

Prerequisites

MATH 155 (College Algebra) with minimum grade of C
Corequisite: CHEM 101 or CHEM 107 (may be taken concurrently)

The Nine Primitives

Before "mathematics" or "chemistry," there is perception. Humans perceive reality through fundamental patterns:

Primitive	The Perception	Tools Summoned	Chemistry Examples
COLLECTION	"There are many"	Sets, counting, factorial	Moles, electron shells
ARRANGEMENT	"Order matters"	Permutations, matrices	Isomers, configurations
DIRECTION	"It points"	Vectors, dot product	Bond angles, dipoles
PROXIMITY	"Near vs. far"	Functions, limits	Potential energy, equilibrium
SAMENESS	"Unchanged"	Symmetry, eigenvalues	Conservation, resonance
CHANGE	"Becoming"	Derivatives, operators	Reactions, transitions
RATE	"How fast"	Derivatives, diff eq	Kinetics, half-life
ACCUMULATION	"All together"	Integrals	Work, total yield
SPREAD	"Distributed"	Probability	Boltzmann, entropy

Key Insight

Mathematics and chemistry are the same thought wearing different clothes.

Required Materials

Textbook: Mathematics for Physical Chemistry, 5th Ed., R.G. Mortimer (Elsevier)
Calculator: Scientific calculator (TI-30X IIS recommended)
Software: Julia + Pluto notebooks (free, installation guide provided)

Student Learning Outcomes

Upon successful completion of this course, students will be able to:

#	Learning Outcome	Level	Assess
1	Identify which cognitive primitive(s) are operating in a given chemical phenomenon	Recognize	E, Q, P
2	Perform vector operations and apply them to molecular geometry and bonding	Apply	E, Q
3	Use matrices to represent transformations and solve systems of linear equations	Apply	E, Q
4	Calculate derivatives and interpret them as rates of change in chemical contexts	Apply	E, Q
5	Evaluate integrals and interpret them as accumulated quantities in chemistry	Apply	E, Q
6	Set up and solve first-order differential equations for kinetic systems	Apply	E, P
7	Apply probability concepts to interpret distributions in chemical systems	Apply	E, Q
8	Select appropriate mathematical tools based on primitive recognition	Analyze	E, P

Assessment key: E = Exam, Q = Quiz, P = Primitive Recognition Portfolio

Assessment and Grading

Component	Weight	Description
Midterm Exam 1 (Structure)	20%	Vectors, matrices; SLOs 1–3
Midterm Exam 2 (Change)	20%	Derivatives, integrals; SLOs 4–5
Weekly Recognition Quizzes	15%	Best 10/12; 10 min at start of Thursday class
Primitive Recognition Portfolio	15%	3 entries; See-Recognize-Tool analysis
Interactive Notebook Assignments	10%	Pluto notebook explorations
Comprehensive Final Exam	20%	Cumulative; all SLOs

Grading Scale

A: 90–100% | B: 80–89% | C: 70–79% | D: 60–69% | F: <60%

Primitive Recognition Portfolio

Three times during the semester, you will submit a 1–2 page analysis following this structure:

THE PHENOMENON: Describe a chemical situation (from your other courses, research, or daily life)
RECOGNITION: Identify which primitive(s) are operating and justify your identification
THE TOOL: Explain which mathematical tool(s) correspond to the primitive(s) and why
APPLICATION: Show how the tool illuminates the phenomenon

Rubric: Primitive identification (30%), Justification (30%), Tool selection (20%), Insight (20%)

Class Format (75 minutes)

Each class follows the Reality → Recognition → Tool cycle:

Time	Phase	Activities
0–3 min	Settle	Attendance, announcements
3–12 min	Retrieval	Quiz (Thu) or recall questions + brief discussion
12–20 min	Hook	Chemical phenomenon: "What do you see?" → Name the primitive
20–40 min	Tool Build	Mathematical content built step-by-step from the primitive
40–60 min	Interactive	Pluto notebook exploration; guided practice with partner
60–72 min	Application	Chemistry connection; problem-solving in pairs
72–75 min	Close	Muddiest point; preview next phenomenon

Course Schedule

Schedule subject to adjustment. Q = Quiz at start of class. All classes follow: Hook → Recognition → Tool → Interactive.

MODULE 1: Structure (Weeks 1–5) "What is a molecule?"

Wk	Day	Topic	Primitive(s)	Tool(s)
1	Tue	Orientation: Seeing Reality	All (intro)	—
1	Thu	What kinds of numbers? How many?	COLLECTION	ℤ→ℚ→ℝ→ℂ, Sets, n!
2	Tue	Arrangements: Isomers and configurations	ARRANGEMENT	Permutations, combinations
2	Thu Q1	Bonds point somewhere	DIRECTION	Vectors in ℝ³
3	Tue	Bond angles and projections	DIRECTION	Dot product, cosine
3	Thu Q2	Molecular coordinates	DIRECTION	Basis, components
4	Tue	Grids of numbers: Data and transformations	ARRANGEMENT	Matrices, operations
4	Thu Q3	What doesn't change?	SAMENESS	Determinants, eigenvalues
5	Tue	Molecular symmetry preview	SAMENESS	Group theory intro
5	Thu	MIDTERM EXAM 1 — SLOs 1–3

MODULE 2: Change (Weeks 6–10) "How do things transform?"

Wk	Day	Topic	Primitive(s)	Tool(s)
6	Tue	As concentration approaches... Limits	PROXIMITY	Functions, limits
6	Thu Q4	Asymptotes and equilibrium — Portfolio 1 due	PROXIMITY	Behavior at boundaries
7	Tue	How fast right now? The derivative	CHANGE	Derivative definition
7	Thu Q5	Rules of change	CHANGE	Differentiation rules
8	Tue	Rates in kinetics	RATE	Rate laws, orders
8	Thu Q6	Higher derivatives; partial derivatives	CHANGE	d²y/dx², ∂f/∂x
9	Tue	Adding it all up: The integral	ACCUMULATION	Integral definition
9	Thu Q7	Integration techniques	ACCUMULATION	Methods
10	Tue	Work, heat, and total yield	ACCUMULATION	∫F·dx, ∫CdT
10	Thu	MIDTERM EXAM 2 — SLOs 4–5

MODULE 3: Dynamics & Probability (Weeks 11–15) "What happens with many particles?"

Wk	Day	Topic	Primitive(s)	Tool(s)
11	Tue	Laws of change: First-order ODEs	CHANGE + RATE	1st order ODE
11	Thu Q8	Radioactive decay; integrated rate laws — Portfolio 2 due	RATE	Exponential solutions
12	Tue	Second-order systems; oscillations	CHANGE	2nd order ODE
12	Thu Q9	Complex exponentials	SAMENESS	Euler's formula
13	Tue	Probability: Sample spaces and distributions	SPREAD	Basic probability
13	Thu Q10	Boltzmann and Gaussian distributions	SPREAD	Distribution functions
— THANKSGIVING BREAK —
14	Tue	Expectation, variance, and error	SPREAD	Moments
14	Thu Q11	Series and approximations	PROXIMITY	Taylor series
15	Tue	Synthesis: The complete map — Portfolio 3 due	All	Full toolkit
15	Thu Q12	Review and exam preparation	—	—
Final	TBA	COMPREHENSIVE FINAL EXAM — All SLOs

How to Succeed in CHEM 291

"You do not know anything until you have practiced." — Richard Feynman

Before Class

Read the assigned section; note what confuses you
Review notes from previous class—especially the primitive and tool
Think: what phenomenon might today's material explain?

During Class

Engage with the hook: What do YOU notice?
Articulate the primitive before the instructor names it
In interactive sessions: change parameters, break things, see what happens

After Class

Same day: Review for 15 minutes; annotate your notebook with the primitive-tool connection
Before next class: Attempt problems without looking at solutions first
Weekly: Find the same primitive in another context (other courses, news, daily life)

What Doesn't Work

Re-reading notes passively (feels productive, isn't)
Memorizing procedures without understanding when to use them
Treating math and chemistry as separate subjects
Looking at solutions before attempting problems (skips the learning)

Course Policies

Attendance and Engagement

Attendance is tracked via PollEverywhere participation. You receive full participation credit with ≥80% attendance—the 20% buffer covers illness, emergencies, and athletics without requiring documentation.

Early support: After 2 missed classes, I'll reach out to check in
Meeting required: After 4 missed classes, we meet to discuss what's getting in the way
Attendance bonus: ≥90% attendance allows dropping lowest midterm exam score

Late Work and Make-ups

Quizzes: No make-ups; lowest 2 scores dropped
Portfolio entries: 10% penalty per day late; not accepted after 3 days
Exams: Make-ups only with documented emergency (thus, the first student to email me the word "eigenvalue" receives 5 bonus points on their first exam); contact instructor BEFORE exam when possible

Technology

Cell phones silenced and out of sight. Laptops permitted only for Pluto notebooks and note-taking.

AI Policy

You may use AI tools (ChatGPT, Claude, etc.) for studying and exploring concepts. However, work submitted for grades must be your own. Using AI to generate portfolio entries or exam answers violates academic integrity. Think of AI like a tutor: great for explaining concepts, but you still have to do your own homework.

Academic Integrity

All work must be your own. Collaboration encouraged for studying; prohibited during exams and quizzes. Portfolio entries must reflect your own recognition and analysis. Violations result in zero for that assessment and are reported to the Dean of Students.

University Policies

Americans with Disabilities Act

Students requiring accommodations should register with the Office of Accessibility Services (Burton Business Center 205A, 337-475-5916, ssd@mcneese.edu). Contact me within the first two weeks to arrange accommodations.

Title IX

McNeese is committed to an environment free from discrimination and harassment. Report concerns to the Title IX Coordinator or confidentially to the Counseling Center.

Mental Health Resources

The Counseling Center (337-475-5956) offers free, confidential support. If you're struggling or concerned about a classmate, please reach out.

Emergency Procedures

Exit via posted routes in emergencies. See mcneese.edu/policy for complete procedures.

Frequently Asked Questions

(Yes, you really should read this section. There may be rewards for those who do.)

Q: I'm not a "math person." Should I be worried?

A: There's no such thing as a "math person." There are people who've had good math experiences and people who haven't—yet. This course is designed to give you a new relationship with mathematics by connecting it to phenomena you can see. Give it a real try before deciding you can't do it.

Q: How is this different from my calculus class?

A: Your calculus class taught you HOW to take derivatives. This course teaches you WHEN to take derivatives—and WHY they're the right tool. We start with the chemistry, not the math.

Q: Do I need to know Julia programming?

A: No prior programming experience needed. Julia is designed to look like math, and Pluto notebooks are reactive—you change a number, everything updates. We'll learn together.

Q: What if I miss a class?

A: Get notes from a classmate, review the posted materials, and come to office hours if confused. The 20% attendance buffer exists because life happens. Use it wisely.

Q: Can I use ChatGPT/Claude for homework?

A: For learning and exploration? Absolutely. For submitted work? That's your brain's job. If you outsource the struggle, you outsource the learning. (Besides, AIs are bad at recognizing primitives—they don't actually see.)

Q: Will there be curves?

A: I don't grade on a curve. You're not competing against your classmates—you're collaborating with them. Everyone who earns an A gets one.

Q: What's a "muddiest point"?

A: At the end of each class, you write down what's still confusing. I read these and adjust the next class accordingly. It's anonymous feedback that helps everyone.

Q: Is there extra credit?

A: The attendance bonus is the extra credit. Attend, engage, and your lowest midterm gets dropped. That's significant.

A Few Chemistry Jokes (Because Math Isn't Always Serious)

Q: Why do chemists like nitrates so much?
A: Because they're cheaper than day rates.

Q: What do you do with a dead chemist?
A: Barium.

Q: Why did the physics teacher break up with the biology teacher?
A: There was no chemistry.

The name's Bond. Ionic Bond. Taken, not shared.

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in."

— Richard Feynman

This syllabus is a guide and may be modified as needed. Changes will be announced in class and on Canvas.

By course end, you will look at any chemical phenomenon and see what kind of thing it is. The math will follow.

I'm looking forward to teaching you to see differently.

— Dr. B

"Never trust an atom. They make up everything."