Math102
Intro to Higher Math
Faculty
Andrey Kechin
Master of Science fellow
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Mathematics is the fundamental foundation of all programming. Mathematical logic was developed long before the invention of the first arithmometer. High school mathematics provides basic knowledge and skills across various areas of the vast and diverse landscape of mathematics. This course is designed to bridge beginners’ understanding with future studies in higher-level mathematics. The Introduction to Higher Mathematics aims to smooth the transition from school-level maths to advanced mathematical concepts.
Learning highlights
- In this intensive course, students will bridge the gap between school and university mathematics, develop formal proof skills, and study combinatorics and logic.
- Familiar topics such as trigonometry and functions will be expanded and enriched with new applications.
- Additionally, new subjects like complex numbers and proof techniques will be introduced briefly.
- Furthermore, students will be introduced to the basics of calculus, binary logic, higher algebra, function analysis, number theory, and set theory.
Course outline
15 classes
Mathematical Logic
Two-level argumentation.
Logical connectives.
Session 2
Functions.
Plotting functions.
Axiomatic approach.
Session 3
Exponents and logarithms.
Trigonometric functions.
Session 4
Complex numbers. Operations on complex numbers. Complex numbers and trigonometry.
Euler number and trigonometric functions.
Session 5
Function analysis.
Complex function and sample space.
Derivatives and integrals on graphs.
Session 6
Fundamental theorem of algebra.
Binomial expansion.
Systems of equations.
Gaussian eliminations
Session 7
Review and Midterm
Session 8
Proving techniques. Proof of existence. Proof by contradiction. Proof by induction.
Session 9
Intro to set theory.
Venn and Euler diagrams.
Sample space.
Session 10
Vectors. Addition and subtraction of two vectors. Dot product. Cross product.
Session 11
Combinatorics. Enumeration and induction. Permutations.
Session 12
Probability.
Simple event. Compound event and combinatorics.
Session 13
Optimization problems.
Estimate and example.
Session 14
General review
Session 15
Final exam
Prerequisites
There are no special skills required for this course.
Methodology
The methodology combines Problem-Based Learning (PBL) and Interactive Visual Learning (IVL) technologies. PBL involves presenting real-world problems and guiding students to apply discrete mathematics concepts such as graph theory and combinatorics to solve them. IVL focuses on using visualisation tools during lectures to enhance understanding.
Each class is typically divided into three parts: Lecture, Active learning (discussion, Q&A), Problem-solving
Students are encouraged to solve a problem during class that builds on the previous homework. Homework is reviewed at the start of the following session.
Exams are split into two parts: theory and practice. Theory accounts for one-third of the total score, and practice two-thirds.
Grading
Andrew graduated from Siberian Federal University and obtained the Master of Science degree in Physics in 2021.
The scientific interests are in biophysics, medicine, and modelling of real biology features in-silico. The master article is devoted to the quantum modelling of an Endothelial Growth Factor Receptor`s ligand as a target for positron emission tomography. Andrew is an awardee of a students olympiad and an active member of a math book translation team.
See full profileApply for this course
Intro to Higher Math
by Andrey Kechin
Total hours
45 Hours
Dates
Sep 08 - Sep 26, 2025
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.