Román Contreras
View the site in Spanish

MSc in Mathematical Sciences · UNAM

Math, physics, and programming tutoring that actually makes sense.

Support for high school, undergraduate, and graduate students. Online from anywhere, or in person in Mexico City.

  • 8

    courses taught at university level

  • High school to grad school

    levels I work with

  • Online or Mexico City

    format

Background

Trained in mathematics, at home in the classroom.

I studied mathematics at UNAM and have been teaching ever since: undergraduate courses, one-on-one sessions, and material made for each student.

Education

  • MSc in Mathematical Sciences

    UNAM

  • BSc in Mathematics

    UNAM

I have also tutored high school students and undergraduates in biology, mathematics, electrical engineering, and geomatic engineering.

University courses I have taught

  • Algebra
  • Analytic geometry
  • Higher algebra I and II
  • Modern (abstract) algebra
  • Differential topology
  • Riemannian geometry
  • Math for biology
  • Math for physicists

What I can teach

From high school to graduate school, and programming too.

Pick the level you care about. If your topic is not on the list, ask me: chances are we can cover it.

Middle and high school

Science and math from your syllabus, plus admission exam preparation.

  • Math: algebra, trigonometry, and calculus
  • Physics
  • Chemistry
  • Biology
  • Admission exam preparation

Undergraduate

Service courses, engineering, and the mathematics major.

  • Differential and integral calculus
  • Linear, abstract, and higher algebra
  • Analytic and differential geometry
  • Differential equations
  • Math for biology
  • Math for physics and engineering
  • Probability and statistics
  • Mathematical analysis
  • Topology

Graduate school and olympiads

Advanced topics, guided reading, and competition training.

  • Differential topology
  • Riemannian geometry
  • Master's-level mathematics courses
  • Math olympiad training
  • Guided reading of texts
  • Thesis and project support

Programming

From first steps to complete projects, with real exercises.

  • Python from scratch
  • Data analysis and visualization
  • Web development: HTML, CSS, and JavaScript
  • Linux and server administration
  • Rust
  • LaTeX and Typst for papers and theses
  • Simulations and animation with Manim

Don't see your topic?Tell me about it

How I work

First you see it, then you write it.

Almost no math topic starts with a formula. It starts with a picture, an experiment, or a concrete problem; the notation comes later, once it means something.

  • Intuition before notation

    Pictures, graphs, and numerical examples so you can see what is happening before formalizing it.

  • Material made for your course

    Short Manim videos, notes, and exercises based on your syllabus and your exams, not on a generic textbook.

  • Code as a lab notebook

    Simulations and visualizations in Python or JavaScript to experiment with the idea and check that it holds.

  • Deliberate practice

    A few well-chosen problems, worked through carefully, instead of endless exercise lists.

“My job isn't to do your homework for you. It's to make sure that next time you can do it yourself, and that you know why it works.”

— Román Contreras

A sample

Math you can touch.

Move the slider and watch the rectangles close in on the exact area under the curve. That is how I usually start: with something you can see and play with before writing a single formula.

Riemann sum
2.656
Exact value
2.667
Error
0.01

∫abf(x) dx≈Σi=1nf(xi) Δx

  1. 1Each rectangle is Δx = (b − a) / n wide.
  2. 2Its height is f(xᵢ), evaluated at the midpoint of each interval.
  3. 3As n grows, Δx approaches zero and the sum approaches the integral.

The same drawing, in a few lines of JavaScript.

const dx = (b - a) / n;
let sum = 0;

for (let i = 0; i < n; i++) {
  const x = a + (i + 0.5) * dx; // midpoint
  const h = f(x);               // height

  drawRect(x, h, dx);           // draw the rectangle
  sum += h * dx;                // add its area
}

// sum ≈ area under the curve

Pricing

Clear pricing, no surprises.

60-minute sessions, online. Book a single session or a discounted package.

Middle and high school

MX$500

per 60-minute session

  • 4-session package

    MX$400 per session

    MX$1,600

  • 8-session packageBest value

    MX$375 per session

    MX$3,000

Book a session

Undergraduate

MX$600

per 60-minute session

  • 4-session package

    MX$500 per session

    MX$2,000

  • 8-session packageBest value

    MX$450 per session

    MX$3,600

Book a session

Graduate school and olympiads

Advanced topics, guided reading, and olympiad training. Pricing depends on the topic and frequency.

Request a quote

Programming

Python, data, web, Linux, or Rust. Pricing depends on the level and the project.

Request a quote

Studying at a public institution? Ask about your discount.

For students at SEP, UNAM, IPN, and UAM with a valid ID. It can be combined with packages.

  • Materials, exercises, and questions between sessions included.
  • Packages valid for 10 weeks.
  • Payment by bank transfer; cancellations 24 hours in advance.
  • Prices in Mexican pesos. In-person sessions in Mexico City are quoted by area and schedule.

FAQ

What people usually ask.

If your question is not here, write to me: I answer personally.

Are sessions online or in person?

Online, over video call with a shared digital whiteboard, from anywhere. In person in Mexico City, depending on availability and area.

How long is a session?

One hour (60 minutes).

How much does it cost?

The pricing section lists the per-session rate and the discounted packages. Graduate school, olympiads, and programming are quoted case by case.

Are there discounts?

Yes. If you study at a public institution (SEP, UNAM, IPN, or UAM) with a valid ID, ask about your discount; it can be combined with packages.

Do I need to prepare anything for the first session?

The course name or syllabus is enough. If you have notes, past exams, or a problem set, bring them: they help pinpoint exactly what to work on.

Can you help if my exam is in two days?

Sometimes, depending on the topic and how far along you are. Write to me as soon as you can and we will figure out what is realistic.

Do you record sessions?

I can, if you give me permission. You can also send me questions by message between sessions.

Do you help with theses or projects?

Yes, especially in mathematics, geometry, data analysis, and programming. We can talk it through in a first conversation.

Contact

Tell me what you need.

Write to me with the course, the level, and your exam date if you have one. I will reply with a plan and a quote.

Monday to Saturday · I reply within 24 hours.

The first conversation is free.