Distance Learning - Pure Mathematics Foundations


Click here for course contents.

The goal of this practical distance course is to provide a solid basis for those professionals who work in computational finance, engineering as well as advanced undergraduate and MSc students who wish to improve their mathematical skills in order to be more productive in their daily work and study. The focus is on several major use cases:

  • Learn the notation and essential concepts of pure mathematics.
  • An incremental approach by taking motivational examples before moving to more advanced topics.
  • Concentrate on the essential aspects: examples, applications and insights. In general, we discuss theorems and their results in detail while in general we refer to other sources for their proofs.
  • Mathematical foundations for specialised courses and application areas.

We wish to ease the learning process and demystify mathematics by making it more accessible to a wide range of students. This course deals with a number of topics up to the second (or third) year of a good mathematics honours degree but it is not meant to be a replacement for it. If you wish the full rigour of mathematics (including theorem proving and more advanced topics) then a degree programme in mathematics would be more suitable.

Originator and Mentor: Dr. Daniel J. Duffy


Subjects Covered

  • Review/refresh of advanced school/college mathematics.
  • How mathematicians solve problems.
  • Algebra and number systems.
  • Real analysis fundamentals.
  • Sequences and series.
  • Functions of several variables.
  • Integration and function spaces.
  • Introduction to Functional Analysis.
  • Discrete Mathematics.
  • Introduction to probability, Markov chans and stochastic differentiation equations.


Course Benefits/What do you learn?

  • Learn the insights to solving mathematical problems (G.  Polya approach).
  • Hands-on experience by working on problems step-by-step; checking your answers against the provided solutions.
  • Becoming comfortable with mathematical notation and applications.
  • Foundation for a career in your profession.


For whom is this Course?

We have developed this course specially for professionals and MSc students who wish to improve their mathematical skills. Prerequisites are mathematical maturity to the level as in Preamble and Review: College/High-School Mathematics part of this course. At the very least you should have seen these topics in a previous life. We review these topics as part of the main course as it were but it is expected that this will not be a challenge for you.

Structure of Course and Student-Trainer Interaction

This course takes an incremental/inductive approach by first examining model problems in detail and then extending them to more advanced applications. Student progress is measured by working on graded exercises. Regular communication takes places by e-mail and Skype.

Students receive a certificate on successful completion of the course.

Course Resources
The course consists of  videos (that you get lifelong access to),  exercises as well as the hard-copies (in pdf format) of the videos.

The optimal way to learn in our opinion is by executing the following steps. This discussion pertains to studying and learning the contents of a single module:
1. Listen to the audio show and use the printed PowerPoint slides as  backup.
2. Read the relevant material in the provided book(s).
3. Do the exercises; compile and run the programs.
4. If you are having problems, go back to one of more of steps 1, 2, 3.
5. If step 4 has been unsuccessful then post your problem on the Datasim forum.
6. Go to next module. 

Click here for course contents.


We give a student discount.  The student price is Euro 1500 and each subsequent course costs Euro 795 (no VAT if you are outside EU). The courses remain accessible forever and you can plan your own schedule but in general it should be possible to complete a course (including exercises and mini-project) in 2-4 months.  See also our Frequently Asked Questions (FAQ) on the Datasim site. Please contact dduffy@datasim.nl

If you are a college student please ignore the price below and contact dduffy@datasim.nl for your student price.

Course price

Price (excl. VAT) € 2832.00
Date Start online course directly

Distance Learning - Pure Mathematics Foundations

Fill in your personal details