What will I study in this module?

In the first semester the module covers

  • Elementary number theory (8 lectures),
  • Matrix arithmetic (8 lectures),
  • Eigenvalues and vectors for 2x2 matrices (8 lectures),
  • Limits and continuity (8 lectures),
  • The derivative of a function (8 lectures),
  • The anti-derivative of a function (8 lectures),
  • and explains how these six topics can be applied to

  • cryptography,
  • geometry/computer graphics,
  • Google page rank,
  • existence of antipodal positions on the Earth's surface with equal air pressure,
  • rates of change problems and maximization problems,
  • prediction of how the world population of humans will grow.

How will the module be assessed?

In the first semester there will be:

  • 40% for quizzes.
    In the last week of the semester there will be two 1-hour quizzes, together worth 40%. Each quiz will consist of three questions. They will be modelled on the past exam paper available here.
  • 40% for homeworks.
    The homework problems are worth 40%. They will be delivered as six online problem sheets which will be made available here. Submission deadlines are strict. There are about 12 questions per problem sheet and to score 100% on the Semester I CA component you need to submit 60 or more correct answers.
  • 20% for group work.
    Students will submit two small-group projects, each worth 10%. Details.

MA180 students

The first semester score will be averaged with the second semester score to obtain an overall score for the 15 credit MA180 module. There will be six more homework sheets in Semester II and students must pass the 12 homeworks on average in order to be eliible to pass the MA180 module.

MA185 students:

The first semester score will be returned as the score for the MA185 Analysis and Algebra module, and will also count for 50\% of the MA187 Mathematical Skills module.

MA190 students:

The first semester score is equal in weight to the second semester analysis and calculus module (though second semester algebra is returned as part of he CT102 module).

Live lectures, on-campus workshops, textbooks, and contact

  • Lecturer: Prof Graham Ellis. (He can be contacted at graham.ellis@nuigalway.ie. Mathematical questions should normally be addressed to your workshop tutor and not to him. Mathematical questions can also be addressed to the people in SUMS.)
  • Lectures: Students can participate in live Zoom lectures at 1pm Mondays, 10am Tuesdays, 10am Wednesdays and 10am Thursdays. The link will be posted on Blackboard and circulated by email to registered students prior to the lectures.

    Lectures will be recorded and the videos will be posted below. So if you happen to miss a live lecture then you can always watch it dead. But any contributions from students during the lectures will not be recorded.
  • Workshops: On-campus workshops begin on Monday 28 September. Details can be found here.
  • Recomended text: The lecture notes and web links (below) and continuous assessment problems contain all material necessary for this module.

    The algebra lectures are based on the e-textbook
    A Short Introduction to University Algebra, by Graham Ellis
    which will be made available on Blackboard.

    The calculus lectures are based on the textbook:
    Calculus, early transcendentals by James Stewart (Sixth Edition).
    Only so much of an explanation can be achieved in lectures, and this book can be used to reinforce (or maybe even clarify!) explanations given in lectures. It also contains many problems (some with fully worked solutions) on which you can practice. Even if you drop maths in second year, this will be a handy book for your scientific bookshelf. And if you continue with maths in second year then you'll be able to use the book again then.
  • Module Website: Information and module documents will be posted to this site, which is linked from the Blackboard Mathematics MA180 & MA185 & MA190 (Semester I) pages. Blackboard will also be used for announcements, quizzes, second semester exams, and for posting grades.

Homework sheets and Deadlines

The online homework sheets are available here.


Friday 16 October, 5pm First Okuson homework sheet
Friday 30 October, 5pm Second Okuson homework sheet
Friday 06 November, 5pm First small-group project
Friday 13 November, 5pm Third Okuson homework sheet
Friday 27 November, 5pm Fourth Okuson homework sheet
Friday 04 December, 5pm Fifth Okuson homework sheet
Friday 11 December, 5pm Second small-group project
Wednesday 16 December, 10am First quiz
Thursday 17 December, 10am Second quiz
Friday 18 December, 5pm Sixth Okuson homework sheet

Recorded lectures and notes

Lecture Notes

click number to view notes
Lecture Videos, Summaries and Other Material

25 September 2020: slides and prerecorded video

This is a talk about first year Mathematics and Mathematical Studies (Science) given as part of Orientation Week.
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Supplementary material

CLICKER OPINION POLLING may be used in some lectures.


This online calculator will help with all your modular arithmetic calculations.


I'm not too sure of the answer. But whatever it is it is possibly something a bit larger than what was taught in your school mathematics classes. If you are interested in the question then you should browse this article by Fields Medallist William Thurston. He won the Fields Medal for his work in geometry. You could also take a look at the lovely little book A Mathematician's Apology by G.H. Hardy which is available online here.


Have a look at this link to answer this question.


A few students have asked for more problems, similar to the homework problems, to practice on. I'll place some here after each homework has closed:


If you are finding the pace of lectures too slow and want to browse some advanced textbooks that cover advanced topics related to material in the lectures then you might take a look at


I'll place student feedback here.

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