Mathematics and Computer Science BSc (Joint Honours)

Year 1 of the programme has been designed as an even split between subjects related to Computer Science and subjects related to Mathematics.

You take the modules

• Introduction to Programming in Java: Introduces you to concepts and principles of problem solving by computer, the construction of algorithms for the solution of problems and their implementation in the high-level programming language Java.
• Introduction to Databases: Introduces you to concepts and techniques for the appropriate and efficient design of databases and database systems and provides you with an understanding and practical experience of data manipulation and query in SQL.
• Computer Systems: Provides you with an overview of the components and operations of computers and their relationship to higher-level software systems.
• Algorithmic Foundations: Introduces you to the terminology and techniques underpinning the study of algorithms and standard algorithmic design paradigms.
• Calculus I: Introduces the basic ideas of differential and integral calculus, the fundamental concepts and techniques of real analysis, and the notions of sequences and series and of their convergence.
• Calculus II: You learn to use Taylor series to obtain local approximations to functions and are introduced to multivariable calculus.
• Introduction to Linear Algebra: You are introduced to techniques of complex numbers and linear algebra.

Plus one of the following two modules

• Dynamic Modelling: Provides you with the basic methods for modelling mathematically topics in subjects like biology, engineering, physical sciences and social sciences.
• Numbers, Groups and Codes: Provides an introduction to group theory and an appreciation of the utility and power of group theory as the study of symmetries.

• Introduction To Programming In Java (COMP101) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 0:100 Aims
• To introduce concepts and principles of problem solving by computer, and the construction of appropriate algorithms for the solution of problems.
  

• ​To demonstrate the principles underlying the design of high level programming languages.
  

• ​ To give students experience and confidence in the use of a high level programming language to implement algorithms.

Learning Outcomes

​ Be able to implement, compile, test and run Java programmes, comprising more than one class, to address a particular software problem.

​ Understand how to include arithmetic operators and constants in a Java program.

​ Be able to make use of members of classes found in the Java API (such as the Math class).

​ Demonstrate the ability to employ various types of selection constructs in a Java program.

​ Demonstrate the ability to employ repetition constructs in a Java program.

Be able to employ a hierarchy of Java classes to provide a solution to a given set of requirements.


​ Demonstrate the ability to use simple data structures like arrays in a Java program.

​ Specific learning outcomes are listed above.




General learning outcomes:

• An understanding of the principles and practice of object oriented analysis and design in the construction of robust, maintainable programs which satisfy their requirements;
• A competence to design, write, compile, test and execute straightforward programs using a high level language;
• An appreciate of the principles of object oriented programming;
• An awareness of the need for a professional approach to design and the importance of good documentation to the finished programs.

 

• Introduction To Databases (COMP102) Level 1 Credit level 15 Semester Whole Session Exam:Coursework weighting 60:40 Aims
  1. To gain an understanding of database systems, encourage the appropriate and efficient design and usage of database systems at the conceptual and logical level;
  2. To provide an understanding and practical experience of of data manipulation and query in SQL;
  3. To provide a basic understanding of relational algebra and its mapping to SQL.
  Learning Outcomes

  At the end of this module the student should be able to

  1. identify principles of conceptual design using ER and UML design methodologies;
  2. apply principles of conceptual design using ER and UML design methodologies;
  3. recognise logical design principles, in particular normalization and functional dependencies;
  4. state the issues related to physical design;
  5. use SQL as a data definition and manipulation language, and as a language for querying databases;
  6. operate and use a basic DBMS;
  7. identify the principles underpinning the relational model and its relationship to SQL;
  8. identify the legal implications of creating and maintaining a database system.
• Computer Systems (COMP103) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims
  •  To introduce how computers function at the instruction operation level.
  • To introduce the relationships between the instruction operation level and both the higher (software) and lower (hardware) levels
  Learning Outcomes

  At the conclusion of the module, students should: 

  • Understand how a computer operates at the machine code level;
  • Understand at an introductory level the structure of computer hardware at the gate and register transfer level;
  • Appreciate the roles and organisation of the major kinds of system software, including operating systems, compilers and system service routines.

   

   

   

• Algorithmic Foundations (COMP108) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims
• To introduce the notation, terminology, and techniques underpinning the study of algorithms.
  

  1. ​ To introduce the standard algorithmic design paradigms employed in the development of efficient algorithmic solutions.

  2. To introduce the mathematical tools needed for the analysis of algorithms in terms of the use of formal models of Time and Space.
  Learning Outcomes describe standard algorithms such as sorting algorithms, search algorithms, string matching algorithms, graph traversal algorithms;

  apply these algorithms or a given pseudo code algorithm in order to solve a given problem;
  

  ​ carry out simple asymptotic analyses of algorithms involving sequence, selection, and iteration, and identify and compare simple properties of these algorithms;

  ​ describe the algorithm design principles of divide-and-conquer, greedy method, and dynamic programming and distinguish the differences between these principles;

  ​ apply the studied algorithms that illustrate these design principles;

  ​ apply the studied design principles to produce algorithmic solutions to a given problem;

  ​ explain and illustrate the distinction between different classes of problems, in particular, polynomial time and exponential time solvable problems.

  3. Calculus I (MATH101) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims

     1.       To introduce the basic ideas of differential and integral calculus, to develop the basic  skills required to work with them and to  apply these skills to a range of problems.

     2.       To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

     3.       To introduce the notions of sequences and series and of their convergence.

     Learning Outcomes

     After completing the module students should be able to:

     ·      differentiate and integrate a wide range of functions;

     ·       sketch graphs and solve problems involving optimisation and mensuration;

     ·       understand the notions of sequence and series and apply a range of tests to determine if a series is convergent.

  4. Calculus Ii (MATH102) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

     ·      To discuss local behaviour of functions using Taylor’s theorem.

     ·      To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

     Learning Outcomes

     After completing the module, students should be able to:

     ·         use Taylor series to obtain local approximations to functions;

     ·         obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

     ·         evaluate double integrals using Cartesian and polar co-ordinates.

  5. Introduction To Linear Algebra (MATH103) Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims
     •      To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
     •      To develop geometrical intuition in 2 and 3 dimensions.
     •      To introduce students to the concept of subspace in a concrete situation.
     •    To provide a foundation for the study of linear problems both within mathematics and in other subjects.
     Learning Outcomes

     After completing the module students should be ableto:

     •     manipulate complex numbers and solve simple equations involving them
     •     solve arbitrary systems of linear equations;
     •     understand and use matrix arithmetic, including the computation of matrix inverses;
     •     compute and use determinants;
     •     understand and use vector methods in the geometry of 2 and 3 dimensions;
     •     calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics.

• Dynamic Modelling (MATH122) Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims

  1. to provide the basic methods for modelling mathematically topics in subjects like biology, engineering, physical sciences and social sciences;

  2. to discuss the advantages of using mathematics in modelling;

  3. to demonstrate some simple models involving differential equations and difference equations;

  
  4. to provide a foundation for an understanding of mechanics. Learning Outcomes

  After completing the module students should be able to:
  

  . solve simple differential equations;

  ·    understand some methods of mathematical modelling and, in particular, the need to attach meaning to mathematical results;

  ·    develop some differential equations for population growth, and interpret the results;

  ·    understand Newton''s laws of Mechanics;

  ·    do simple problems in projectiles and orbits, some involving polar co-ordinates.

• Numbers, Groups and...