School of Computing Science

# School of Computing Science

### CSC1025 : Mathematics for Computer Science

• Offered for Year: 2016/17
• Module Leader(s): Dr Jason Steggles
• Demonstrator: Miss Laura Heels
• Lecturer: Dr Victor Khomenko
• Other Staff: Dr Jennifer Warrender
• Owning School: Computing Science
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 20 ECTS Credits: 10.0

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#### Aims

To develop confidence in the use of simple mathematics.
To provide a knowledge of the mathematical concepts essential for study and professional practice in Computing Science and Software Engineering.
To revise key areas of basic mathematics.
To practice the basic techniques of mathematics for modelling and solving computing problems.
To prepare students for the more advanced mathematics they will encounter on their degree.
To develop an awareness of the role of mathematics in Computing Science.

This module introduces the key mathematical skills needed in computing science. It revises key areas of basic mathematics and covers important topics in discrete mathematics. The module aims to develop the students confidence in using basic mathematical techniques.

#### Outline Of Syllabus

Discrete Structures – functions relations and sets
- Functions (surjections, injections, inverses, composition)
- Relations (reflexivity, symmetry, transitivity, equivalence relations)
- Sets (Venn diagrams, complements, Cartesian products, power sets)
- Pigeonhole principle
Discrete Structures – basic logic
- Propositional logic
- Logical connectives
- Truth tables
- Normal forms (conjunctive and disjunctive)
- Validity
- Predicate logic
- Universal and existential quantification
- Modus ponens and modus tollens
- Limitations of predicate logic
Discrete Structures – proof techniques
- Notions of implication, converse, inverse, contrapositive, negation, and contradiction
- The structure of mathematical proofs
- Direct proofs
- Proof by counterexample
- Mathematical induction
- Recursive mathematical definitions
Discrete Structures – basics of counting
- Counting arguments
- Sum and product rule
- Arithmetic and geometric progressions
- Fibonacci numbers
- Permutations and combinations
- Basic definitions
- Pascal’s identity
- The binomial theorem
Discrete Structures – graphs and trees
- Trees
- Undirected graphs
- Directed graphs
Other
- Matrices and vectors.
- Real-valued functions, exponential growth/decay, logarithms, derivative, min/max, equations.
- Number representations, binary conversion, GCD, Euclid’s algorithm.

#### Learning Outcomes

##### Intended Knowledge Outcomes

To comprehend a range of key mathematical topics, including:
- set theory;
- numbers and their representation;
- functions and relations;
- matrices and vectors;
- combinatorics and counting;
- mathematical proof;
- graph theory;
- propositional and predicate logic.

##### Intended Skill Outcomes

- To choose appropriate mathematical techniques to aid problem solving.
- To manipulate mathematical expressions.
- To employ mathematical structures to model design problems.
- To prove mathematical properties.
- To apply learnt techniques to solve a range of mathematical problems.

• Cognitive/Intellectual Skills
• Critical Thinking : Assessed
• Data Synthesis : Assessed
• Active Learning : Present
• Numeracy : Assessed
• Self Management
• Self Awareness And Reflection : Present
• Planning and Organisation
• Goal Setting And Action Planning : Present
• Decision Making : Assessed
• Personal Enterprise
• Innovation And Creativity : Present
• Independence : Present
• Problem Solving : Assessed
• Interaction
• Communication
• Written Other : Present
• Team Working
• Collaboration : Present
• Peer Assessment Review : Present

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion12:002:00End of semester examination
Guided Independent StudyAssessment preparation and completion440:3022:00Revision for end of semester exam
Guided Independent StudyAssessment preparation and completion401:0040:00Lecture follow-up
Scheduled Learning And Teaching ActivitiesLecture401:0040:00Lectures
Scheduled Learning And Teaching ActivitiesSmall group teaching241:0024:00Tutorials
Guided Independent StudyProject work221:0022:00Coursework
Total200:00
##### Teaching Rationale And Relationship

Lectures will be used to introduce the learning material and for demonstrating the key concepts by example. Students are expected to follow-up lectures within a few days by re-reading and annotating lecture notes to aid deep learning.

Tutorials will be used to emphasise the learning material and its application to the solution of problems and exercises set as coursework, during which students will analyse problems as individuals and in teams.

Students aiming for 1st class marks are expected to widen their knowledge beyond the content of lecture notes through background reading.

Students should set aside sufficient time to revise for the end of semester exam.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
PC Examination1201A80N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M202 pieces worth 8% each and one worth 4% (up to 20 hours total)
##### Assessment Rationale And Relationship

The PC exam will be used to assess students' knowledge, understanding and ability to apply the key mathematical topics covered in the course.
The coursework assignments will be used to help develop and assess students' understanding of and abilities to apply core mathematical techniques introduced within the course.

Study abroad students considering this module should contact the School to discuss its availability and assessment.

N.B. This module has both “Exam Assessment” and “Other Assessment” (e.g. coursework). If the total mark for either assessment falls below 35%, the maximum mark returned for the module will normally be 35%.

#### General Notes

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Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.