Mathematics in the Modern World

Bulacan State University
San Rafael Campus

This page contains lecture notes, examples, exercises, and supplementary material for Mathematics in the Modern World, prepared primarily for the BS Biology students whom I teach. This is not just a mathematics appreciation course. This version of MMW places more emphasis on calculation and mathematical reasoning than students may expect from a general-education course. It may feel challenging at times, but the work is intended to stretch students rather than overwhelm them. This emphasis follows the broad scope of Mathematics in the Modern World described in CHED Memorandum Order No. 20, series of 2013, while adapting the material to the needs of biology students.

The course has two aims. The first is to develop practical mathematical literacy—including financial literacy—that students can use in everyday life. The second is to introduce a little of several areas of mathematics in preparation for more advanced quantitative courses. Contrary to popular opinion, there is a great deal of mathematics in biology, so examples are drawn whenever possible from biology, ecology, health, and data analysis.

Biological and medical research is highly interdisciplinary. Students are not expected to master every field, but knowing something about different mathematical and computational approaches helps them recognise what a problem calls for—and whom they might ask to collaborate with, whether a statistician, mathematical modeller, computer scientist, or another specialist.

I generally think of this as a challenging but enjoyable course. At a time when so much can feel uncertain, I hope students can find, as I do, some solace in mathematics: definitions can be made clear, assumptions stated, and conclusions followed step by step. Mathematics has easy and difficult parts, just like any other field, but it has acquired an undeservedly nasty reputation. Much of the fear surrounding it begins with that reputation, unfamiliar notation, or an earlier bad experience rather than with the subject itself. It takes practice, but it is not reserved for geniuses. I am not a genius; I learnt mathematics in the same way most people learn anything difficult—by studying, making mistakes, and trying again.

Logistics

Course title: Mathematics in the Modern World
Course number: MMW 101
Term: First Semester, A.Y. 2026–2027
Instructor’s name: Rey Joseph Nieto
Email: rj (at) rjnieto (dot) com (for questions or inquiries related to the course)
Consultation hours: To be announced through official class channels
Class schedule and room: Refer to the official class schedule

Important dates

Assessment	Date
Midterm examinations	To be announced through official class channels
Final examinations	To be announced through official class channels

Printable lecture notes

The current version of the complete lecture notes is available as a PDF.

Open the MMW 101 lecture notes

Current version: 22 August 2026

House rules

Printed notes are available if you need them. If you do not have reliable access to a laptop or mobile device, speak to me after class or during consultation hours. You do not need to explain your circumstances; I will provide the relevant printed notes free of charge.
Attend regularly and arrive on time. Much of our learning will happen through explanation, discussion, and guided work in class, and attendance contributes to the final mark under the syllabus and university policy. The notes are a guide rather than a transcript: our pace, examples, and order may change. Any change affecting examinable material will be announced clearly; you will not be assessed on an unannounced topic.
Participate, ask questions, and seek help. Questions are welcome in class, by email, and during consultation hours; longer or off-syllabus discussions are usually best saved for consultation. You will not be judged for finding something difficult. Ask classmates, compare notes, and come to me when something remains unclear. You do not have to struggle alone.

NoteLanguage in our classroom

The notes use British English. The differences between British and American English are relatively subtle in this course, apart from some spelling conventions and a few terms, so they should not cause difficulty. Either is acceptable if your meaning is clear and consistent. Practising English will help with the biology literature, but it is not a barrier to participation. Students may use any dialect of Tagalog or Cebuano, or English. Questions in other languages are also welcome when someone can help translate. If my accent or wording is difficult to follow, tell me—I can explain in Taglish whenever practicable.
Expect biology to involve mathematics. Population growth, inheritance, epidemics, ecological networks, experimental uncertainty, medical images, and protein structures all involve mathematical thinking. You will not be asked to train an artificial neural network; the goal is to recognise quantitative structure, interpret evidence, and reason carefully. These skills matter in biology and medicine as well as in ordinary decisions.

NoteA case in point: mathematics and biology

My BSc Mathematics thesis used computational topology to turn structures in retinal photographs into numerical summaries and test their reliability under changes such as blur, rotation, and noise. It brings together mathematics, computation, and medical imaging. Curious readers can explore the public thesis or the project repository; the advanced mathematics is not required for this course.
Be present and considerate. I have no interest in teaching through fear, and questions are always welcome. In return, help maintain a respectful room: listen when someone is speaking and avoid side conversations. Giving one another our attention makes those “Wow, talaga?” moments much easier to reach.
Bring a notebook and a pen. Record definitions, ideas, examples, and questions in your own words rather than copying everything. After class, practise active recall: reconstruct the main ideas from memory, then check what you missed. Compare notes with classmates and ask me about gaps that remain.

NoteUse of generative AI

Generative-AI tools can provide another explanation, suggest practice questions, or offer a different perspective. Use them cautiously: they can sound convincing while being wrong, so check their claims against the notes and do the mathematics yourself. They cannot replace independent understanding and will not be available during graded assessments.
Work steadily, but keep marks in perspective. Assessments will be proportionate to the available time and published criteria. I will identify enrichment as examinable or non-examinable, and examinations will not hide “curveball” topics whose status was unclear. You may still be asked to apply a familiar idea in a new setting. Quizzes and recitations will be announced and completed in class. Work steadily, and use feedback to improve. Have faith in your ability—I do.
Read the notes before class. I will aim to publish each set of notes at least two weeks before we cover it. You are not expected to master the material beforehand: skim the headings, notice the main ideas and examples, and bring any questions that arise. Mathematics can be difficult, but it becomes more approachable when studied steadily, explained patiently, and connected to meaningful problems.
Correct mistakes—respectfully. Address the idea, never embarrass the person. Please point out errors in the notes or in anything I say; a valid mathematical or factual correction may earn extra credit under criteria applied equally to everyone. Finding a mistake is not a challenge to my authority—it helps improve both the notes and the class, and I will be glad you raised it.