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diff --git a/md/research/edi-math.md b/md/research/edi-math.md new file mode 100644 index 0000000..da6c6c3 --- /dev/null +++ b/md/research/edi-math.md @@ -0,0 +1,310 @@ +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__ + + diff --git a/md/research/math.md b/md/research/math.md index 6a055bd..ec17b56 100644 --- a/md/research/math.md +++ b/md/research/math.md @@ -6,5 +6,6 @@ keywords:math,university,research ## Universities [Open University](./ou-math.md) [Oxford University](./oxford-math.md) +[Edinburgh University](./edi-math.md) |