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

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