Math101
Intro to Higher Mathematics
Faculty
Serhii Denysov
Senior algorithms R&D at drawer.ai, Programming and math university teacher.
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
The idea of mathematics as the language of the universe (a shortened version of Galileo’s phrase) is reaffirmed time and again through our technological advances. The human brain also appears to be naturally aligned with mathematics – or perhaps vice versa. Yet, for many people, learning maths can be challenging. The transition from school-level maths to higher mathematics – with its notions of infinity, formal proofs, and increased abstraction – can present a significant hurdle in the learning journey.
The aim of this course is to support students in making that transition smoother and to help them feel more confident with the concepts, ideas, and notation that will be encountered and developed in mathematically intensive courses such as calculus, algebra, probability, and scientific computing.
Learning highlights
- Ability to read, write, and comprehend higher mathematical notation.
- Ability to think logically and reason about mathematical objects used in calculus, algebra, probability theory, and applied mathematics.
- Basic understanding and practical skills in working with real numbers, sets, functions, polynomials, trigonometry, summation, inequalities, and related topics.
- Ability to construct mathematical proofs using inference, induction, and contradiction.
Course outline
15 classes
Session 1
Overview of higher mathematics. School math refresher.
Session 2
Numbers. Rational and real numbers. Idea of infinity and infinitesimal quantities.
Session 3
Functions. Decartian plane. Plotting function graph. Selected properties of function.
Session 4
Polynomials, exponents, logarithms and trigonometric functions. Graphical representations. Fundamental identities.
Session 5
Complex numbers. Operations. Relation to trigonometric functions.
Session 6
Proving techniques and notation. Quantifiers. Proof of existence. Proof by contradiction. Proof by induction.
Session 7
Solving inequalities. Inequalities with trigonometric and exponential / logarithmic functions.
Session 8
MidTerm Exam
Session 9
Complex roots of polynomials. Fundamental theorem of algebra. Binomial expansion.
Session 10
Idea of vectors. 2D vectors. Operations. Dot product. Basics of nD vectors.
Session 11
System of equations. Elimination procedure.
Session 12
Summation. Finite and infinite sums. Infinite sequences. Idea of a limit. Progressions.
Session 13
Basics of combinatorics. Permutations and combinations.
Session 14
Intuition of probability. Simple and compound event.
Session 15
Final Exam.
Prerequisites
Familiarity with basic mathematics is expected, including arithmetic, variables, equations, fundamental geometry, and the Cartesian coordinate system.
Methodology
Practice-oriented sessions centred around topic discussions, occasional programming elements, and a substantial amount of homework.
Grading
Serhii has worked in the software engineering industry in different positions for many years. Roles included software developer, system architect, IT consultant, project manager and CTO. He is also an experienced educator and is always glad to help students learn how to start having fun with programming and math and become top-level software developers or R&D engineers.
He has taken part in a long row of business automation projects for different businesses, with many small and several big projects, such as one of the biggest outdoor advertising agency in Ukraine and a country-wide software cash registers company, processing millions of transactions per day. Now he is a senior algorithms R&D in a highly dynamic startup drawer.ai.
See full profileApply for this course
Intro to Higher Mathematics
by Serhii Denysov
Total hours
45 Hours
Dates
Sep 08 - Sep 26, 2025
Fee for single course
€1500
Fee for degree students
€750
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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.