title:OU Math Courses keywords:math,ou # OU Math Courses ## Intro Researching what kind of difference between few undergraduate programmes is available at OU (OpenUniversity). Compare how they are different and similar. In future to compare them with other universities. Also to make decision choice on with one to choose based on most topics interested in or not known. Q31 - BSc (Honours) Mathematics Q36 - BSc (Honours) Mathematics and Statistics R38 - BSc (Honours) Data Science Q15 - BSc (Honours) Economics and Mathematical Sciences ## Stages This is list of modules that is possible to choose on each of the stage. Each stage represents year in brick uni. As all stages could be taken as any speed as possible. ### Stage 1 ``` DS (R38) - TM111, MST124, M140, TM112 M (Q31) - MU123, MST124, M140, MST125 MS (Q36) - MU123, MST124, M140, MST125 ES (Q15) - MU123, MST124, M140, DD126 ``` ### Stage 2 DS - M248, M249, M269, MST224, M - M208 (M248, MST210, MST224) MS apl - M248, M249, MST210 MS pure - M248, M249, M208 ES - DD209, M248, MST224 ### Stage 3 DS - (M343) (M347) M348, (M373) (MT365) (TM351) TM358 (TM356) M - M303 !M337 !M343, M346, M347, M373, MS327, MT365 ME620 MST326 SMT359 SM358 MS apl - (M337) M343, M346, M347 (M373) (MS327) (MT365) (ME620) (MST326) MS pure - (M337) M343, M346, M347 (M373) (MS327) (MT365) (ME620) ES - (M337) (M343) M346, (M373) (MS327) (MT365) DD309 ## Selected path ### Similarity ## Topics All modules and topics covered in each of modules ### TM111 Introduction to computing and information technology 1 http://www.open.ac.uk/courses/qualifications/details/tm111?orig=r38 ### TM112 Introduction to computing and information technology 2 http://www.open.ac.uk/courses/qualifications/details/tm112?orig=r38 ### MU123 Discovering mathematics http://www.open.ac.uk/courses/qualifications/details/mu123?orig=q15&setAcc=true ### MST124 Essential mathematics 1 http://www.open.ac.uk/courses/qualifications/details/mst124?orig=q31 ### MST125 Essential mathematics 2 http://www.open.ac.uk/courses/qualifications/details/mst125?orig=q31 ### DD126 Economics in context http://www.open.ac.uk/courses/qualifications/details/dd126?orig=q15 #### Block 1 This provides a detailed historical analysis of how the UK economy, and its interactions with other economies, has changed since the 1700s. You'll look at some of the reasons why the Industrial Revolution occurred in the UK at that time. It also explores the themes of the module: change, agents and success, navigating through events in economic history, and in economics as a discipline. #### Block 2 In this block you'll explore the market and the role of markets in societies. The view of economics that looks at economic agents and their motives in isolation is the foundation to thinking about markets as the interactions between these agents, and their measures of success; and also how markets operate within economies that have organised themselves, and their main economic activities, in particular ways. You'll look at the competitive model of the market and as economists often analyse formal models using diagrams a key skill in the economist s toolkit extensive use of demand and supply diagrams is made to explain how the model works. #### Block 3 This third block looks at economies in a more holistic way, critically reflecting on the best way of organising economic activities, and striking a balance between market activity and government intervention. The key areas that are explored are employment, industry and trade. You'll return to discussions of economics across time and place to explore the experiences and evolution of markets under different types of economic systems. This block will also give you the chance to measure and explain success through the use and collection of data sources, which is another important skill in the economist s toolkit. ### M140 Introducing statistics http://www.open.ac.uk/courses/qualifications/details/m140?orig=q31 #### Unit 1 Looking for patterns The basic idea of statistical modelling and the modelling diagram Stemplots The shape (skewness, modes) of data sets Median and range #### Unit 2 Prices Mean, weighted mean, quartiles, interquartile range Five-figure summary Simple ideas of index numbers UK consumer price indices (CPI, RPI) #### Unit 3 Earnings Earnings ratios Percentile and deciles Boxplots Deviations, variance and standard deviation Average Weekly Earnings index and comparing changes in prices and earnings #### Unit 4 Surveys Basic ideas of survey sampling Simple random sampling, Systematics sampling, General ideas of stratification and clustering, Quota sampling Sampling errors #### Unit 5 Relationships Relationships, scatterplots, response and explanatory variables Describing relationships Lines and residuals. Least squares regression #### Unit 6 Truancy Basic ideas of probability Combining probabilities (addition and multiplication rules) Steps in a hypothesis test The sign test p-values and interpreting significance test results #### Unit 7 Factors affecting reading The normal distribution One- and two-sample z-tests #### Unit 8 Teaching how to read Contingency tables. Joint and conditional probabilities The chi-squared test in contingency tables Type 1 and type 2 errors #### Unit 9 Comparing schools Causality and association Correlation. Outliers and influential points Confidence intervals and prediction intervals #### Unit 10 Experiments Basic ideas of scientific experimentation One- and two-sample t-test (one and two-sided) Matched pairs t-test Calculating confidence intervals #### Unit 11 Testing new drugs Drug testing and clinical trials Types of design for trials (group comparative, matched pairs, crossover) Phases of drug trials, post-marketing surveillance #### Unit 12 Review Using Minitab to carry out straightforward data analyses ### M208 Pure mathematics http://www.open.ac.uk/courses/qualifications/details/m208?orig=q31 #### Unit A1 Sets, functions and vectors Revises important foundations of pure mathematics and the mathematical language used to describe them. #### Unit A2 Number systems Systems of numbers most widely used in mathematics: the integers, rational numbers, real numbers, complex numbers and modular or 'clock' arithmetic, and looks at when and how certain types of equations can be solved in the system. #### Unit A3 Mathematical language and proof Writing of pure mathematics and some of the methods used to construct proofs, and as a further introduction to abstract mathematical thinking equivalence relations are introduced. #### Unit A4 Real functions, graphs and conics Reminder of the principles underlying the sketching of graphs of functions and other curves. #### Unit B1 Symmetry and groups Symmetry of plane figures and solids, and shows how this topic leads to the definition of a group, which is a set of elements that can be combined with each other in a way that has four basic properties called group axioms. #### Unit B2 Subgroups and isomorphisms Subgroups, which are groups that lie inside other groups, and also at cyclic groups, which are groups whose elements can all be obtained by repeatedly combining a single element with itself. It also investigates groups that appear different but have identical structures. #### Unit B3 Permutations Functions that rearrange the elements of a set: it shows how these functions form groups and looks at some of their properties. #### Unit B4 Lagrange's Theorem and small groups Fundamental theorem about groups, and uses it to investigate the structures of groups that have only a few elements, before focusing on improving skills in understanding theorems and proofs in the context of group theory. #### Unit C1 Linear equations and matrices Why simultaneous equations may have different numbers of solutions, and also explains the use of matrices. #### Unit C2 Vector spaces Generalises the plane and three-dimensional space, providing a common structure for studying seemingly different problems. #### Unit C3 Linear transformations Mappings between vector spaces that preserve many geometric and algebraic properties. #### Unit C4 Eigenvectors Diagonal representation of a linear transformation, and applications to conics and quadric surfaces. #### Unit D1 Numbers Real numbers as decimals, rational and irrational numbers, and goes on to show how to manipulate inequalities between real numbers. #### Unit D2 Sequences The 'null sequence' approach, used to make rigorous the idea of convergence of sequences, leading to the definitions of pi and e. #### Unit D3 Series Convergence of series of real numbers and the use of series to define the exponential function. #### Unit D4 Continuity Sequential definition of continuity, some key properties of continuous functions, and their applications. #### Unit E1 Cosets and normal subgroups Revision of Units B1-B4 and looks at how a group can be split into 'shifts' of any one of its subgroups. #### Unit E2 Quotient groups and conjugacy How to 'divide' a group by one of its subgroups to obtain another group, and how in any group some elements and some subgroups are similar to each other in a particular sense. #### Unit E3 Homomorphisms Functions that map groups to other groups in a way that respects at least some of the structure of the groups. #### Unit E4 Group actions How group elements can sometimes be applied to elements of other sets in natural ways. This leads to a method of counting how many different objects there are of certain types, such as how many different coloured cubes can be produced if their faces can be painted any of three different colours. #### Unit F1 Limits The epsilon-delta approach to limits and continuity, and relates these to the sequential approach to limits of functions. #### Unit F2 Differentiation Differentiable functions and gives L'Hopital's rule for evaluating limits. Integration explains the fundamental theorem of calculus, the Maclaurin integral test and Stirling's formula. #### Unit F3 Integration The fundamental theorem of calculus, the Maclaurin integral test and Stirling's formula. #### Unit F4 Power series Finding power series representations of functions, their properties and applications. ### DD209 Running the economy http://www.open.ac.uk/courses/qualifications/details/dd209?orig=q15 ### MST210 Mathematical methods, models and modelling http://www.open.ac.uk/courses/qualifications/details/mst210?orig=q31 ### MST224 Mathematical methods http://www.open.ac.uk/courses/qualifications/details/mst224?orig=q31 ### M248 Analysing data http://www.open.ac.uk/courses/qualifications/details/m248?orig=q31 ### M249 Practical modern statistics http://www.open.ac.uk/courses/qualifications/details/m249?orig=q36 ### M269 Algorithms, data structures and computability http://www.open.ac.uk/courses/qualifications/details/m269?orig=r38 ### M303 Further pure mathematics http://www.open.ac.uk/courses/qualifications/details/m303?orig=q31 #### Chapter 1 Foundations Proof by induction, divisibility, linear Diophantine equations #### Chapter 2 Prime numbers Prime numbers, Fundamental Theorem of Arithmetic, prime decomposition of integers, the theta-function, Fibonacci numbers. #### Chapter 3 Congruence Definition of congruence, properties of congruence, divisibility tests, linear congruences, solution of linear congruences, solving systems of linear congruences. #### Chapter 4 Fermat's and Wilson's Theorems Fermat's Little Theorem, Wilson's Theorem, polynomial congruences, Lagrange's Theorem (for numbers) #### Chapter 5 Examples of groups Group axioms, subgroups, cosets, Lagrange's Theorem (for groups), normal subgroups, quotient groups, conjugate elements, homomorphism of groups, isomorphism of groups, first isomorphism theorem, correspondence theorem. #### Chapter 6 Towards classification Direct product of groups, internal direct product theorem, cyclic groups, direct product of cyclic groups, decomposition of finite cyclic groups, group actions, orbits and stabilisers. #### Chapter 7 Finite groups Group presentations, dihedral groups, dicyclic groups, #### Chapter 8 The Sylow Theorems Sylow p-subgroup, the Sylow theorems, applications of the Sylow theorems, prime power subgroups theorem. #### Chapter 9 Multiplicative functions Multiplicative functions, Euler's phi-function, reduced set of residues, Euler's theorem, primitive roots. #### Chapter 10 Quadratic reciprocity Solutions of quadratic congruences, quadratic residues, Euler's criterion, the Legendre symbol, Gauss's Lemma, quadratic character of 2, the law of quadratic reciprocity, quadratic character of 3, the Jacobi symbol. #### Chapter 11 Rings and polynomials Ring axioms, subrings, units, fields, polynomials over fields, division algorithm for polynomials, factors of a polynomial, Euclidean algorithm for polynomials, factorising polynomials, irreducibility for polynomials, rational root test, Gauss's lemma, Eisenstein's criterion #### Chapter 12 Fermat's Last Theorem and unique factorisation Pythagorean triples; integral domains; associates, irreducibles and primes in rings; integral domains, norms for integral domains; Euclidean domains; division algorithm for Euclidean domains; highest common factors in Euclidean domains; unique factorisation domains. #### Chapter 13 Distance and continuity Sequences in the real line; real null sequences; continuity of real-valued functions; intermediate value theorem; extreme value theorem; continuity on the plane; Euclidean distance on the plane. #### Chapter 14 Metric spaces and continuity 1 Continuity of functions from R^n to R^m, Euclidean distance on R^n, convergent sequences in R^n, metrics, metric spaces, convergence of sequences in metric spaces, continuity in metric spaces. #### Chapter 15 Metric spaces and continuity 2 Induced metrics, Cantor metric, equivalent metrics, product metrics, pointwise convergence of functions, uniform convergence of functions, the max metric on C[0,1]. #### Chapter 16 Open and closed sets Open sets, closed sets, dense sets, nowhere dense sets, closure of a set, interior of a set, boundary of a set, countable sets, uncountable sets. ##### Chapter 17 Rings and homomorphisms Fields of fractions, ring isomorphisms, primitive polynomials, ideals, principal ideals, principal ideal domain, algebra of ideals, cosets of an ideal, quotient rings, ring homomorphisms, maximal ideals, prime ideals. #### Chapter 18 Fields and polynomials Isomorphism of fields, field extensions, vector spaces over fields, degree of a field extension, algebraic and transcendental elements, minimal polynomials, the KLM Theorem for field extensions, finite fields, roots of unity, splitting fields, splitting polynomials, classification of finite fields. #### Chapter 19 Fields and geometry Subfield generated by a set, field extensions of finite degree, field of algebraic numbers, transcendental extension, ruler and compass constructions, constructible number, impossibility of doubling the cube, squaring the circle and trisecting the angle pi/3 #### Chapter 20 Public-key cryptography RSA cryptosystem, Diffie-Hellman cryptosystem, elliptic curves, Diffie-Hellman-ElGamal cryptosystem, Menezes-Vanstone cryptosystem. #### Chapter 21 Connectedness Homeomorphisms, disconnections, connectedness, connected components, totally disconnected sets, connectedness in Euclidean spaces, the intermediate value theorem, path-connectedness, the topologist's cosine. #### Chapter 22 Compactness Sequential compactness, the Heine-Borel theorem, generalised extreme value theorem, Arzela-Ascoli Theorem, open covers, compact metric spaces, equivalence of sequential compactness and compactness in metric spaces. #### Chapter 23 Completeness Cauchy sequences, complete metric spaces, the contraction mapping theorem, completion of a metric space. #### Chapter 24 Fractals The Hausdorff metric, self-similar sets, iterated function schemes, box dimension, open set condition. ### DD309 Doing economics: people, markets and policy http://www.open.ac.uk/courses/qualifications/details/dd309?orig=q15 ### MST326 Mathematical methods and fluid mechanics http://www.open.ac.uk/courses/qualifications/details/mst326?orig=q31 ### MS327 Deterministic and stochastic dynamics http://www.open.ac.uk/courses/qualifications/details/ms327?orig=q31 ### M337 Complex analysis http://www.open.ac.uk/courses/qualifications/details/m337?orig=q31 ### M343 Applications of probability http://www.open.ac.uk/courses/qualifications/details/m343?orig=q31 ### M346 Linear statistical modelling http://www.open.ac.uk/courses/qualifications/details/m346?orig=q31 ### M347 Mathematical statistics http://www.open.ac.uk/courses/qualifications/details/m347?orig=q31 ### M348 Applied statistical modelling New ### TM351 Data management and analysis http://www.open.ac.uk/courses/qualifications/details/tm351?orig=r38 ### TM356 Interaction design and the user experience http://www.open.ac.uk/courses/qualifications/details/tm356?orig=r38 ### SM358 The quantum world http://www.open.ac.uk/courses/qualifications/details/sm358?orig=q31 ### TM358 Machine learning and artificial intelligence New ### SMT359 Electromagnetism http://www.open.ac.uk/courses/qualifications/details/smt359?orig=q31 ### MT365 Graphs, networks and design http://www.open.ac.uk/courses/qualifications/details/mt365?orig=q31 ### M373 Optimization http://www.open.ac.uk/courses/qualifications/details/m373?orig=q31 ### ME620 Mathematical thinking in schools http://www.open.ac.uk/courses/qualifications/details/me620?orig=q31 ## Literature recommended to read List of literature that are recommended in source or a course text book. ## Links