path: root/md/research/edi-math.md

title:Edinburgh University Math Courses
keywords:math,edinburgh,university

# Edinburgh University Math Course

https://www.ed.ac.uk/studying/undergraduate/degrees/index.php?action=programme&code=G120

https://www.ed.ac.uk/studying/undergraduate/degrees/index.php?action=programme&code=GG14

https://www.ed.ac.uk/studying/undergraduate/degrees/index.php?action=programme&code=G100

https://www.ed.ac.uk/studying/undergraduate/degrees/index.php?action=programme&code=GG13


Course list

http://www.drps.ed.ac.uk/22-23/dpt/cx_sb_math.htm

By subject

https://www.ed.ac.uk/global/study-abroad/course?browseby=subject&browsebysubject=Mathematics


## Topics

### MATH10086	Advanced Methods of Applied Mathematics	 

http://www.drps.ed.ac.uk/22-23/dpt/cxmath10086.htm


### MATH10077	Algebraic Topology	

http://www.drps.ed.ac.uk/22-23/dpt/cxmath10077.htm


### MATH10053	Applied Stochastic Differential Equations	

http://www.drps.ed.ac.uk/22-23/dpt/cxmath10053.htm


### MATH08058	Calculus and its Applications	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08058.htm

### MATH10072	Combinatorics and Graph Theory	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10072.htm

### MATH10017	Commutative Algebra	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10017.htm

### MATH08065	Computing and Numerics	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08065.htm

__Course description__

The course will cover:
- Creation and manipulation of arrays
- Solutions of linear systems
- Gaussian elimination with partial pivoting
- Numerical differentiation and integration
- Introductory numerical differential equations
- Root finding methods, including bisection and fixed-point iteration
- Newton's method in one and higher dimensions
- Functional minimization in multiple dimensions

Within these topics students will be introduced to:
- Variables and functions
- Floating point arithmetic
- Flow control
- Container types
- Plotting
- Symbolic expressions

__Reading list__  
S. Linge and H. P. Langtangen, Programming for Computations  Python, Springer, 2016  
P.R. Turner, T. Arildsen, and K. Kavanagh, Applied Scientific Computing with Python, Springer, 2018  

### MATH10099	Entrepreneurship in the Mathematical Sciences	
https://www.drps.ed.ac.uk/22-23/dpt/cxmath10099.htm

### MATH10047	Essentials in Analysis and Probability	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10047.htm

### MATH08068	Facets of Mathematics	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08068.htm

### MATH10003	Financial Mathematics	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10003.htm

### MATH10051	Fourier Analysis	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10051.htm

### MATH07003	Fundamentals of Algebra and Calculus	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath07003.htm

### MATH10065	Fundamentals of Operational Research	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10065.htm

### MATH08064	Fundamentals of Pure Mathematics		 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08064.htm

__Course description__

Analysis:
Real Numbers; Inequalities; Least Upper Bound; Countable and Uncountable Sets; Sequences of Real Numbers; Subsequences; Series of Real Numbers; Integral, Comparison, Root, and Ratio Tests; Continuity; Intermediate Value Theorem; Extreme Values Theorem; Differentiability; Mean Value Theorem; Inverse Function Theorem.

Algebra:
Symmetries of squares and circles; Permutations; Linear transformations and matrices; The group axioms; Subgroups; Cyclic groups; Group actions; Equivalence relations and modular arithmetic; Homomorphisms and isomorphisms; Cosets and Lagrange's Theorem; The orbit-stabiliser theorem; Colouring problems.

__Reading List__

Groups, by C. R. Jordan and D. A. Jordan  
Kenneth Ross, Elementary Analysis.  

### MATH10080	Galois Theory	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10080.htm

### MATH10076	General Topology	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10076.htm

### MATH10074	Geometry	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10074.htm

### MATH10079	Group Theory	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10079.htm  

__Summary__	
This is a course in abstract algebra, although connections with other fields will be stressed as often as possible. It is a systematic study of the basic structure of groups, finite and infinite.  
__Course description__	
- Homomorphisms, isomorphisms, and factor groups
- Group presentations and universal properties
- Sylow theorems and applications
- Simple groups and composition series
- Classification of finite abelian groups and applications
- Solvable groups and the derived series


__Reading list__
The course notes will be the main reference, although :  
M A Armstrong, Groups and Symmetry (QA171 Arm ) is a subsidiary reference. Other references include  

T S Blyth and E S Robertson, Groups (QA171.Bly)  
J F Humphreys, A Course in Group Theory (QA177 Hum)  
J J Rotman, The theory of groups: An introduction (QA171 Rot )  
J J Rotman, An introduction to the Theory of Groups (QA174.2 Rot )  


### MATH10069	Honours Algebra	 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10069.htm

### MATH10068	Honours Analysis		 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10068.htm

### MATH10067	Honours Complex Variables		 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10067.htm

### MATH10066	Honours Differential Equations	 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10066.htm

### MATH08057	Introduction to Linear Algebra		 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08057.htm  

__Course description__
	This syllabus is for guidance purposes only:
The course will have a range of student-focused activities equivalent to approximately three lecture-theatre-hours and a 90 minute Example Class per week. The course contents are given in the course textbook, Nicholson, predominantly Chapters 1 to Chapter 5, and the start of Chapter 8, with a selection (not all) of the applications covered and selected topics omitted.

- Vectors in R^n, and in general. Vectors and geometry
- Systems of linear equations, echelon form, Gaussian elimination, intro to span and linear independence.
- Matrices, multiplication, transpose, inverses, linear maps. Intro to subspaces and bases. Rank.
- Eigenvalues and eigenvectors. Determinants
- Orthogonality, Gram-Schmidt, orthogonal Diagonalization.
- Introduction to abstract vector spaces and subspaces.
- Selected applications (taught in sequence where appropriate)

__Reading List__
Students will require a copy of the course textbook. This is currently "Linear Algebra with Applications" by W. K. Nicholson. This is available freely as a PDF, and print-on-demand, physical copies are available. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.

### MATH10071	Introduction to Number Theory	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10071.htm  

__Course description__
1. Binary operations on integers, axioms of a ring.

2. The ring of integers Z. The division algorithm. Euclidean algorithm. Primes, units, irreducibles in Z. Irreducibles in Z are primes in Z. Factorisation in integers. The Fundamental Theorem of Arithmetic.

3. Rings. Axioms of a ring. Deducing some basic properties from axioms, for example deducing that the zero element in any ring is unique. Using rings to prove some basic results from elementary number theory.

5. Integral domains, zero divisors. Cancellation in domains. Greatest common divisor.
6. Gaussian integers and rings Z[d] where d is some irrational number. Units, primes, irreducibles in such rings. Using properties of the ring of Gaussian integers to determine which integers can be written as sums of squares of two integers.

7. Ideals in rings. Factor rings. Examples of rings.

8. Euclidean domains. Uniqueness of factorisation. Primes and irreducibles in Euclidean domains. Euclidean algorithm for Euclidean domains. The ring of Gaussian integers is a Euclidean domain.

9. Connections of Gaussian integers and quadratic residues and the Legandre symbol.

10. Exercises on the Legandre symbol and quadratic residues. We will solve a variety of questions on quadratic residues using the five basic rules of calculating quadratic residues. We will assume some results such as Gauss Lemma and the Law of Quadratic residues without proofs and will concentrate on being able to use them for calculating the Legendre symbol in a variety of exercises. We will mention surprising connections of the Legendre symbol and Gaussian integers.

11. Applications of previous material to linear and quadratic congruences. Linear and quadratic congruences. We will apply the obtained results on Legandre symbol to determine how many integer solutions have some quadratic congruences. We will apply the Euclidean algorithm to solve linear congruences.

12. Euler's function. We will apply the formula for Euler's function in the solving of a variety of exercises. Let n be an integer larger than 0. The Euler's function gives the number of integers which are larger than zero and not exceeding n and are co-prime with n.

__Reading List__

- Elementary Number Theory, by Kenneth H. Rosen, 6th Edition, 2010, Pearson.
- A friendly introduction to number theory by J. H. Silverman, Prentice Hall, 2001.
- Introduction to number theory by Lo-keng Hua, Springer-Verlag, 1982.

### MATH10100	Introduction to Partial Differential Equations	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10100.htm

__Course description__

__Reading List__

### MATH07004	Introductory Mathematics with Applications		 	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath07004.htm  

__Course description__

The central topics are as follows:
1. Quadratic functions and their graphs.
2. Polynomials, functions, graphs, and their inverses.
3. Mathematical reasoning and writing mathematical arguments.
4. Exponential and logarithmic functions.
5. Trigonometric functions using radian measure.
6. The circle (its geometry, as an implicit algebraic function, and as a parametric trigonometric function).
7. Simultaneous equations (2 linear equations, or linear and quadratic), algebraic and graphical methods for solution.
8. Arithmetic and geometric sequences and series.
9. The binomial theorem, and binomial coefficients.
10. Calculus concepts: notion of limit, rate of change, and area.

__Reading List__

The main course material will be presented online. Additional references will be given to outside online material.

### MATH10082	Linear Analysis	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10082.htm  

__Course description__

__Reading List__

### MATH10073	Linear Programming, Modelling and Solution	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10073.htm  

__Course description__

__Reading List__

### MATH10013	Mathematical Biology	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10013.htm

### MATH10010	Mathematical Education	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10010.htm

### MATH10101	Metric Spaces	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10101.htm

### MATH10064	Multivariate Data Analysis	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10064.htm


### MATH10098	Numerical Linear Algebra	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10098.htm  

__Course description__

Linear Algebra is one of the most widely used topics in the mathematical sciences. At level 8 or 9 students are taught standard techniques for basic linear algebra tasks including the solution of linear systems, finding eigenvalues/eigenvectors and orthogonalisation of bases. However, these techniques are usually computationally too intensive to be used for the large matrices encountered in practical applications. This course will introduce students to these practical issues, and will present, analyse, and apply algorithms for these tasks which are reliable and computationally efficient. The course includes significant lab work using an advanced programming language. The course studies three main topics: the solution of linear systems of equations, the solution of least squares problems and finding the eigenvectors and/or eigenvalues of a matrix.

__Reading List__

Numerical Linear Algebra and Applications, Second Edition", by B. N. Datta, SIAM, ISBN: 978-0-898716-85-6  
Numerical Linear Algebra by Lloyd "Nick" Trefethen and David Bau III, SIAM, ISBN: 978-0898713619  
Applied numerical linear algebra by James "Jim" Demmel, SIAM, ISBN: 978-0898713893  

### MATH10060	Numerical Ordinary Differential Equations and Applications	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10060.htm

### MATH08066	Probability	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08066.htm

### MATH10024	Probability, Measure & Finance		 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10024.htm

### MATH08059	Proofs and Problem Solving	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08059.htm

### MATH08063	Several Variable Calculus and Differential Equations	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08063.htm

### MATH10093	Statistical Computing	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10093.htm

### MATH10095	Statistical Methodology	 
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10095.htm

### MATH08051	Statistics (Year 2)	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath08051.htm

### MATH10007	Stochastic Modelling	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10007.htm

### MATH10028	Theory of Statistical Inference	
http://www.drps.ed.ac.uk/22-23/dpt/cxmath10028.htm

__Course description__

__Reading List__