Pure Maths   -   Level 2
MATH 2015 - Analysis 2	This modules is compulsory for Year 2 Mathematics students, and is a continuation of MATH1035 Analysis 1.
MATH 2033 - Rings, Polynomials and Fields	This module builds on topics covered in group theory and linear algebra, and is a prerquisite for MATH3193/5193, MATH3285, MATH5285, and MATH5245.
MATH 2040 - Mathematical Logic 1	Even though this module has no modules as prerequisite, it requires an understanding of formal mathematical language and proof writing. It is very abstract. Leeds offers a wide range of modules in logic at the higher level, and this one is essential for all of them.
MATH 2051 - Geometry of Curves and Surfaces	This modules builds on topics covered in calculus and linear algebra. The objects of study are curves and surfaces. It is a prerequisite for modules in differential geometry.
MATH 2080 - Further Linear Algebra	This module builds on MATH 1060, and is prerequisite for a number of level 3 modules. (only for Math. Studies, Maths with Finance, and Joint Honours students)
MATH 2090 - Real and Complex Analysis	This module covers the basic core of analysis, the theoretical foundations for calculus and differential equations. (only for Math. Studies, Maths with Finance, and Joint Honours students)
MATH 2210 - Introduction to Discrete Mathematics	This module introduces combinatorial concepts relating to counting problems, graph theory, and the abstract notion of computable functions.

Applied Maths   -   Level 2
MATH 2340 - The Mathematics of Music	This is an essay-based module which aims to discuss how mathematics has affected the science and culture of musical theory and composition.
MATH 2391 - Nonlinear Differential Equations	This module builds on techniques from MATH1970 or similar and introduces new methods for solving equations.
MATH 2410 - Special Relativity	This module uses mechanics and vector calculus to describe remarkable physical phenomena, and is a pre-requisite for the level 3 general relativity module.
MATH 2420 - Multiple Integrals and Vector Calculus	(only for Math. Studies and Joint Honours students) This module continues the study of ordinary differential and integral calculus in two and three dimensions. It is essential for the further study in many areas of applied mathematics.
MATH 2431 - Fourier Series, Partial Differentail Equations, and Transforms	(only for Math. Studies and Joint Honours students) This module covers Fourier series and Fourier and Laplace transforms and their applications to the solution of classical Partial Differential Equations of real-world problems in mathematical physics.
MATH 2600 - Numerical Analysis	Although knowledge of a computing language is not necessary, this module will interest students with an interest in using computers to aid mathematical solutions.
MATH 2620 - Fluid Dynamics	This module is a prerequisite for many modules in astrophysical and geophysical fluid dynamics at higher level.
MATH 2650 - Calculus of Variations	This module extends ideas of maximizing and minimizing to more complicated situations, and fundamental results are applied to many real-world problems.

Statistics   -   Level 2
MATH 2715 - Statistical Methods	We recommend the following bundles of modules, depending on your interests. If you have only a passing interest in Statistics, but wish to keep your options open, take at least one of MATH2715, MATH2735.  This will mean you have sufficient prerequisites for at least half of the level 3 modules in Statistics.  MATH2715 takes a more mathematical approach to statistical methods, while MATH2735 is more concerned with practical issues of using statistical techniques to model data. If you have a moderate interest in Statistics, we recommend that you take both MATH2715 and MATH2735, and possibly one semester 2 Statistics module as well. If you wish to specialise in Statistics, we recommend that you take MATH2715 and MATH2735 plus at least 2 of the semester 2 modules. In addition, if you have particular interest in financial applications, you should take MATH2750, even if you take no other Statistics modules this year.
MATH 2735 - Statistical Modelling
MATH 2740 - Environmental Statistics
MATH 2750 - Introduction to Markov Processes
MATH 2770 - Medical Statistics

Consider the following modules if you are interested in the Teaching of Mathematics

• MATH 2800 - Maths into Schools. There is an info meeting for this module on 27.April 2009 at 11am in the Leonard Rogers room (Level 8 School of Maths).
  
• EDUC 2071 - School Mathematics from an Advanced Undergraduate Perspective.

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A few things to keep in mind:

• MMath students are encouraged to think about their plans for Year 4 when choosing modules for Year 3.
  
• Some modules are not offered every year. Check the list below for what is currently planned to be offered in which years.
• Some level 3 modules are "co-taught" with a level 5 module.  This usually means that they have common lectures, but students taking the module at level 5 have some extra material to work through, and take a different exam. MMath students can only take either the level 3 or the level 5 version of such a module.
  
• In addition to the modules listed below, the following project modules are available (depending on the rules for your programme):
• MATH3000 Information Skills in Mathematics (10 credits over Semester 1 & 2)
• MATH3082 Project in Pure Mathematics 1 (15 credits, Semester 1)
• MATH3083 Project in Pure Mathematics 2 (15 credits, Semester 2)
• MATH3422 Project in Applied Mathematics (15 credits, Semester 1 & 2)
• MATH3752 Project in Statistics 1 (15 credits, Semester 1)
• MATH3753 Project in Statistics 2 (15 credits, Semester 2)
• MATH5082 Assignments in Pure Mathematics (35 credits, Semester 1 & 2)
• MATH5422 Assignments in Applied Mathematics (35 credits, Semester 1 & 2)
• MATH5812 Assignments in Statistics (35 credits, Semester 1 & 2)

Pure Maths   -   Level 3 & 5
General Area	Modules
Algebra and Number Theory	MATH 3044 Number Theory MATH 3071 Groups and Symmetry MATH 3171 Algebra and Numbers (only for Joint Honours and Mathematical Studies students) MATH 3193/5193 Algebras and Representations MATH 3152 Coding Theory MATH 5245 Fields and Galois Theory (not running in 2009/10) MATH 5253 Commutative Algebra and Algebraic Geometry
Analysis & Topology	MATH 3181 Inner Product and Metric Spaces (only for Joint Honours and Mathematical Studies students) MATH 3215 Hilbert Spaces and Fourier Analysis MATH 3224 Topology MATH 5015 Linear Analysis 1 MATH 5016 Linear Analysis 2
Discrete Mathematics	MATH 3032 Graph Theory MATH 3142 Combinatorics MATH 3152 Coding Theory
Geometry	MATH 3024 Homotopy and Surfaces MATH 3112/5031 Differential Geometry MATH 3232 Transformation Geometry MATH 5253 Commutative Algebra and Algebraic Geometry
Mathematical Logic	MATH 3102/5102 Mathemtical Logic 2 MATH 3123/5123 Set Theory (not running in 2009/10) MATH 3163/5163 Computability and Unsolvability MATH 3285/5285 (Basic) Model Theory

Statistics   -   Level 3 & 5  - to be offered in 2009/10
MATH 3713/5713 (Robust) Regression and Smoothing	For students taking only a small component of statistics, we recommend choosing from the "core" modules of MATH3713, MATH 3723, andMATH3802.  Other statistics modules cover more specialised areas of statistics. If you are interested in finance, take MATH3733 and MATH3802. If you are interested in bio-medical applications of statistics, take MATH3880  (plus MATH5840 if you are doing the MMath). For MMath students, we recommend that you do not take the level 3 version of these modules but take the level 5 versions instead; this can be in your third or fourth year.  Taking the level 5 versions in your third year will not disadvantage you and will allow you to take a greater number of credits in Statistics overall. Students wishing to specialise exclusively in statistics at level 5 should note that separate M.Sc. degrees in Statistics and Statistics with Applications to Finance are available at Leeds.  If you might be interested in pursuing this option instead of taking the MMath, please speak to a member of the Statistics Department as you need to make appropriate module choices in year 3. Finally, notice that if you take enough credits in Statistics modules then you may, if you wish, graduate with Statistics as your degree title instead of Mathematics. You may also qualify for the status of GradStat, the first step to being awarded Chartered Statistician status.  Please ask if you wish to know more about these options.
MATH 3723 Statistical Theory
MATH 3733 Stochastic Financial Modelling
MATH 3802/5802 Time Series/and Spectral Analysis
MATH 3823/5823 Generalized Linear Models / and Survival Ananlysis
MATH 3880/5880 (Introduction to) Statistics and DNA
MATH 5835 Statistical Computing
MATH 5840 Hidden Markov Models for Biological Sequence Analysis