MA4001 - Logic and Problem Solving (2017/18)
|Module specification||Module approved to run in 2017/18|
|Module title||Logic and Problem Solving|
|Module level||Certificate (04)|
|Credit rating for module||30|
|School||School of Computing and Digital Media|
|Total study hours||300|
|Running in 2017/18||
The module gives students systematic ways of solving problems as well as introduces them to a range of ideas in mathematical logic. It also gives some grounding in standard software packages.
The module aims to give the students an understanding of how problems can be solved systematically, plan their solutions and write them in the form of algorithms. This module also develops a range of mathematical techniques including set theory, logic, relations and functions. In addition it gives a grounding in standard software packages (e.g., spreadsheets or databases), to give students an understanding of their use in problem solving as well as to make students able to apply these packages appropriately in subsequent modules.
- Puzzles: developing logical reasoning, introducing systematic approach to solving puzzles, developing appropriate strategies to solve puzzles
- Propositional Logic:representation of simple verbal arguments; truth-tables; logical equivalence, validity and consequence,logic circuits. Predicate logic.
- Sets: introduction to notation; set operations; Venn diagrams; universal, empty set and subsets; set identities (De Morgan etc); duality; power sets, ordered pairs and Cartesian products.
- Algorithms: understanding how problems can be solved systematically, plan their solutions and write them in form of algorithms (e.g Euclid's Algorithm)
- Combinatorics: combinations, permutation and probability
- Relations: representations of relations (matrix and digraph); equivalence relations; partitions; partial orderings.
- Functions: ways of defining functions; composition; inverse functions.
- Linear Programming, Maths of Finance and Break-even analysis
Learning and teaching
Learning technologies will be used for providing the teaching materials (e.g. WebLearn). The module will be taught by a mixture of lectures, supervised computer laboratory sessions and self study practical exercises. In particular, the lectures will be used to introduce the various concepts and principles of the module's topics or demonstrate worked examples. Each lecture will be followed by a practical supervised session where the students will be able to apply/experiment with the various notions introduced in the lectures, using examples and following detailed instructions. The materials that will be used in the practical sessions will allow each student to work at his/her own speed. Furthermore, students will be pointed to self-study exercises which they will attempt in their own time. The students will also be expected to spend time on private study and on preparation for the assessments.
LO1 Create algorithmic methods of real-world problems, and to develop and present the solutions.
LO2 Understand the meaning of mathematical definitions of sets/propositions and perform set/logic operations.
LO3 Understand the meaning of mathematical definition of relations and to determine which relations are equivalence relations.
LO4 Understand the meaning of mathematical definition of functions, to use it to construct functions and to determine which functions are one-to-one.
This module is assessed through tests and coursework.
In the first test the students are assessed on sets and logic (LO2).
The test and feedback is administered early in the module so that students can identify any deficiencies in their learning strategies and put corrective strategies in place at an early point in their studies. The other test will assess an increasing amount of the syllabus. (LO3 to LO4).
The final component will be group coursework to assess algorithmic methods of real-world business problems (LO1). Coursework assesses topics other than logic. Reassessment coursework can be an individual submission.
Feedback will be given after the first test so that students will have the opportunity to improve their performance in the second test.
Maureen Sprankle, Problem Solving & Programming Concepts, Prentice Hall.
Rod Haggarty, Discrete Mathematics for Computing, Addison Wesley.