Discrete Mathematics and Mathematical Reasoning
This module runs in the first semester. Lecture hours are:
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Monday 17:10-18:00, HRB LT (Lecture Theatre, Hugh Robson Building).
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Wednesday 11:10-12:00, LT1 7BSQ (Lecture Theatre 1, 7 Bristo Square).
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Thursday 17:10 - 18:00, HRB LT (Lecture Theatre, Hugh Robson Building).
The first lecture will take place on Monday 17. September.
Summary of intended learning outcomes
- Reason mathematically about basic (discrete) structures (such as numbers, sets, graphs, and trees)used in computer science.
- Use of mathematical and logical notation to define and formally reason
about mathematical concepts such as sets, relations, functions, and
integers, and discrete structures like trees, graphs, and partial
orders;
- Evaluate elementary mathematical arguments and identify fallacious reasoning
- Construct inductive hypothesis and carry out simple induction proofs;
- Use graph theoretic models and data structures to model and solve some
basic problems in Informatics (e.g., network connectivity, etc.)
- Prove elementary arithmetic and algebraic properties of the integers,
and modular arithmetic, explain some of their basic applications in
Informatics, e.g., to cryptography.
- Compare the asymptotic growth growth rates of basic functions; derive
asymptotic bounds, and limits, for simple series and recurrence
relations. Use these to derive bounds on the resource consumption
(e.g., running time) of simple iterative and recursive algorithms.
- Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations.
- Be able to construct discrete probability distributions based on
simple combinatorial processes, and to calculate the probabilities and
expectations of simple events under such discrete distributions.
Coursework
Weekly
tutorial sheet exercises.
Discussed in tutorial groups.
The last exercise on each tutorial sheet is
marked, and students must submit the solution to the ITO
by the due date each week (see
here).
Grading
The final exam counts for 85%, and the assessed assignments count
(marked tutorial sheet questions) count for 15%.
This page is maintained by the course lecturers Dr. Kousha Etessami and
Dr. Richard Mayr.
