### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title FOUNDATIONS OF COMPUTER SCIENCE Code COMP109 Coordinator Prof B Konev Computer Science Boris.Konev@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2017-18 Level 4 FHEQ First Semester 15

### Aims

1. To introduce the notation, terminology, and techniques underpinning the discipline of Theoretical Computer Science.
2. To provide the mathematical foundation necessary for understanding datatypes as they arise in Computer Science and for understanding computation.
3. To introduce the basic proof techniques which are used for reasoning about data and computation.
4. To introduce the basic mathematical tools needed for specifying requirements and programs

### Learning Outcomes

Understand how a computer represents simple numeric data types; reason about simple data types using basic proof techniques;

Interpret set theory notation, perform operations on sets, and reason about sets;

Understand, manipulate and reason about unary relations, binary relations, and functions;

Apply logic to represent mathematical statement and digital circuit, and to recognise, understand, and reason about formulas in propositional and predicate logic;

Apply basic counting and enumeration methods as these arise in analysing permutations and combinations.

### Syllabus

1. Number systems and proof techniques: natural numbers, integers, rationals, real numbers, prime numbers, proof by contradiction and proof by induction.
2. Approaches to describing collections of objects: sets and set operations, unary and binary relations, properties of binary relations, partial orders and equivalence relations, inverse relations, and compositions of relations.
3. Functions: properties of functions, inverse functions and compositions of functions, the pigeonhole principle.
4. Propositional logic: syntax and construction of formulas, semantics, interpretations and truth tables, tautologies, contradictions, semantic consequence and logical equivalence
5. Combinatorics: notation for sums, products, and factorials, Binomial coefficients, counting permutations, subsets, subsequences and functions.
6. Discrete Probability: sample spaces, events, conditional probability, independence, random variables and expectation.

### Teaching and Learning Strategies

Lecture - Students will be expected to attend three hours of formal lectures in a typical week.

Students are expected to spend at least one hour per week for completion of practical exercises

Tutorial - One hour of tutorials accompany lectures in a typical week

### Teaching Schedule

 Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL Study Hours 30 Students will be expected to attend three hours of formal lectures in a typical week. 12One hour of tutorials accompany lectures in a typical week 42 Timetable (if known) Students are expected to spend at least one hour per week for completion of practical exercises Private Study 108 TOTAL HOURS 150

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Unseen Written Exam  2 hours  80  Yes  Standard UoL penalty applies  Final Exam Notes (applying to all assessments) This CA work is not marked anonymously. Practical assessment is employed for both formative assessment and summative assessment. Students will get short formative feedback on a weekly basis from the module demonstrators during tutorial / lab sessions. More detailed summative and formative feedback will be returned following assessment of the continuously assessed (CA) work. Resit exam will replace failed CA components, the Learning Outcomes will be covered in the resit exam.
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework  6 hours  10  Yes  Standard UoL penalty applies  A combination of assessed homework and in-class coursework 1
Coursework  6 hours  10  Yes  Standard UoL penalty applies  A combination of assessed homework and in-class coursework 2