math at uni

8/14/2019 math at uni

1/24

Start to finish your guide to

maths at university


2/24


3/24

Why study maths at university?

Getting into university tostudy maths

Choosing a university

Maths at university ... at a glance

Maths at university

Mathematical topics at university

Where to getanswers

Look at the university and departmentalwebsites. These will contain the

answers to many of the questions you

might have.

Consult the online or printed

prospectuses for the courses you are

interested in.

Ask questions of staff and, where

possible, students at open days.

If you still have unanswered questions,

talk to the admissions tutor.

4

6

10

14

16

20


4/24

Questions youshould askWhat do graduates from this course

do after their degree?

What proportion of graduates get

jobs within six months of leaving

this course? What proportion go on

to further study?

Does this course help me

to develop skills such asteam-working, IT skills, making

presentations and writing reports?

What will I get

from a maths

degree?

In a maths degree, obviously you learn lotsof maths(!), sometimes as a continuationof your school maths and sometimes incompletely new areas. Exactly what mathsyou meet will depend on the university yougo to and what choices you make duringyour degree.

The mathematical topics you learn aboutare important for some future careers butthere are other things you will learn which

have a wider application and which are muchsought after by a wide range of employers.These include the ability to think logically, toconstruct coherent arguments, to understandabstract ideas and concepts and to solvepractical problems.

In many universities you will also gainexperience in key skills which mostemployers consider important, for examplemaking presentations, writing reports,

team-work and use of computers.


5/24


6/24

Do I have to be agenius to study

maths?

Some people believe that you have to bebrilliant to study maths at university. It iscertainly true that some aspects can be veryabstract and some universities have highentry requirements but most mathematiciansare not geniuses and there are plenty ofordinary people successfully doing maths!

What A level

results do I need?

Entry requirements for any degree varyenormously from university to university. Youdo notneed to get a high A level grade tostudy maths, although obviously a top gradewill give you a wider choice of university.Most university websites will give you an ideaof the offers they make.

Most universities accept some otherqualifications as equivalent to A level forexample the International Baccalaureate is

widely respected.

I dont have anA level in maths

can I stillstudy maths atuniversity?

If you dont have A level maths or anequivalent qualification, most universitieswould require you to do some further studyin maths before starting on a maths degree.Preparatory years (sometimes calledfoundation years) run by many universitiesand Access to HE courses run by FE

colleges are both designed to bring yourmaths up to the required standard.

Some mature students may be able to geta place because of prior experience. Talk tothe admissions tutor about the possibilities.

The Open University (www.open.ac.uk)has no entry requirements for its part-timedegrees.


7/24

Questions youshould ask

What is the typical UCAS offer for this

university?

Is Further Maths recommended?

What percentage of students have

Further Maths? If this is a substantial

proportion, is there additional help

for students without it? Do studentswithout Further Maths get results

comparable to those with it?

Do I need to do STEP/AEA to gain a

place at this university?

What is the departments attitude to

students taking a gap year?

If you are enquiring without

A level maths or equivalent, does

the university run a preparatory

year?

Scottish

qualificationsMuch of the content of this booklet isapplicable to maths courses across theUK. However some of the commentsabout entry qualifications or length ofcourse apply primarily to students fromEngland, Wales or Northern Ireland, orthose students from Scotland with A levelsor Scottish Advanced Highers, applying touniversities in England, Wales or Northern

Ireland.

Degree courses in Scotland, where Highersare the main entrance qualification, aretypically a year longer than elsewhere inthe UK. Students with A levels or AdvancedHighers may be able to gain admissiondirectly into the second year of Scottishcourses, which are broadly equivalent tothe first year of other UK courses. Consultthe university websites for more information.

Do I need FurtherMaths A level tostudy maths at

university?

No. That said, it certainly wont do anyharm! At some universities, FurtherMaths, at least to AS level, is stronglyrecommended. At many others it is unusualfor students to have done Further Maths.


8/24

AmandaAge 42, Second year,

BSc Mathematics

Amanda is married with three sons and a daughter.I studied GCSE maths as an adult to help my children with homework. Wanting to improve my career prospects,I then took an Access course at a local college followed by a preparatory year at university and am now in thesecond year of a maths degree course. Although at times it has been a steep learning curve, I am now completelyhooked on maths I really love it. Amongst other alternatives, I am considering going into adult educationwhen I finish, hopefully to persuade other adults that they can still learn no matter what their age or educationalbackground.

Do I need to takeSTEP or AEA tostudy maths at

university?

A very small number of universities may ask

you take a Sixth Term Exam Paper (STEP)or Advanced Extension Award (AEA) as partof their conditional offer. If so you will begiven support in preparing for these and willfind there are several helpful websites. Youmay find these stimulating, enjoyable andhelpful for your A level study, even if you arenot required to take the exam.

Can I take agap year beforestudying maths?

There is an urban myth that mathematiciansdont take gap years. This is not the case;many maths students take a year betweensixth form and university. Although you mayfind you forget some of your A level maths,a little revision should quickly compensatefor this.


9/24

To fnd out more about Maths degrees, Further Maths and Maths careers please visit:www.moremathsgrads.org.uk, www.fmnetwork.org.uk and www.mathscareers.org.uk


10/24

Are all maths

degrees the

same?

No. There is a nationally agreed standardfor maths degrees but it only specifies twotopics which every course must containso there is plenty of scope for universities

to offer very different things. Even withthe same outline syllabus, universitiescan approach topics in very differentways, for example by having a differentbalance between theoretical and practicalapproaches.

Which maths

degree is best for

me?

This depends on lots of things, includingwhat interests you, your views on classsizes and the level of support you might get,how you feel about the use of technology

in maths, whether you want a wide choiceof topics, whether you want to combinestudying maths with another subjectand what you want to do after university.Research what is on offer carefully, usingthis booklet as a guide.

Ann-MarieAge 23, Final year,

BSc Mathematics

When Ann-Marie first left college, with A levelsin Maths, Psychology and General Studies, she

already knew that she wanted to be a mathsteacher. She started maths at one university butunfortunately found at first that it wasnt for her.So a year later I started afresh at a differentuniversity. Here we use much more technology andthere are many more ways to apply your learning not just exams. That really suited me, but I guessyou have to be happy to be using computers a lot todo maths here.

Not all maths courses are the same. I thinkits about finding a teaching style that suits youpersonally not everyone is the same.

Ann-Marie did a placement with Royal Mail as thethird year of her degree and found it helped her inher final year.

Its been hard work this year but going onplacement helped a lot. My grades went up in thefinal year compared to my second year. I think myplacement helped me learn how to apply myselfand work regularly and gave me extra motivation.

Although Ann-Marie found her placement useful,it hasnt distracted her from her original ambitionof being a maths teacher and shes lookingforward to starting a PGCE course in September.


11/24

What are the

different routes to

a maths degree?

The majority of maths students study full timefor three years and obtain a bachelors degree(BA or BSc) but this is not the only option.Some universities offer a four-year course

leading to a masters qualification (MMath orMSci). This allows you the opportunity to studyto a more advanced level. Transferring fromthe bachelors to the masters route or viceversa is sometimes possible, depending onthe university.

Many universities offer part-time studyand some, especially the Open University,specialise in this. In this case it will take morethan three years to complete your course

and part-time students are not eligible for thesame financial support.

Some universities encourage or requirestudents to do a sandwich course wherestudents typically spend a year gainingvaluable work experience (and getting paid!)often between their second and third year ofstudy.

In addition, at some universities it is possible

to study for up to a year abroad, broadeningyour horizons and improving your languageskills. Sometimes this is in addition to yourhome university studies and sometimes it is inplace of part of it.


Is the course very theoretical andabstract or mainly practical and

applied? What examples can they give

you to demonstrate this?

Does the degree contain a

work-experience placement (sandwich

degree)? Is it optional or compulsory?

What do students do? What help is

given to find a placement? What are the

benefits of doing it?

Can I combine studying maths with

studying another subject?

Can I transfer between different maths

courses within the same university?

What restrictions are there on changing

courses?

Is it possible to study at a university

abroad for some of the time?

How research-orientated is this

department? What difference will this

make to me?

How much choice do I get about the

topics I study?

How many staff are there in the

department and how many students?

Are some classes taught by

postgraduate students or postdocs?


12/24

Can I study maths

with another

subject?

Many universities offer courses whichcombine maths with another subject,for example finance, business, physics,computing or economics. For combinedhonours courses (those with two ormore subjects), most universities use aconvention that if the degree title combinestwo subjects with the word and, eachsubject is given equal weight whereas if thetwo subjects are joined with the word with,you would study the first topic for two-thirdsof your time and the second topic forone-third. So Maths and Computing isequal amounts of each but Maths withFinance is two-thirds maths and one-thirdfinance. When maths is combined with alanguage, it is often required that you spenda year abroad as par t of your study.

In some universities you can change yourcourse after you arrive, although changingfrom combined honours to single honours

maths is often not possible (withoutrepeating the first year) because you wonthave studied all the required first-yeartopics.

How big is

the maths

department?

Maths departments vary in size from ahandful of staff to over 100 and studentnumbers vary enormously too. Bigdepartments can often offer a wider rangeof topics, giving you more choice particularlyin your later years. Small departments maybe more personal and friendly.

DanielleAge 21, Final year,

BSc Mathematics

with Business

Finance

Danielle had always been good at and fond of maths throughoutschool and college but she decided tocombine studying maths with business

management for her degree.

I thought it would be more interesting thanmaths on its own and that the combinationwould open more employment doors for mepost-gradation.

She found the variety interesting and says itbroke up my timetable. She enjoyed learningabout different types of maths and exploringthe diverse range of maths but was surprised tofind how much computing was included in thecourse.

Initially she found it strange being in such bigclasses: the lectures contained about 200people which was quite daunting in comparisonto a lesson in college. I felt like a little fish in abig pond and appreciated the smaller exampleclasses where postgraduate students wereavailable to offer help.

She says her final year has been the best outof the three. I felt the work was a lot easier andI had a grasp of the modules and the level of

maths. I also have a lot more motivation as Ilook forward to graduation.

After graduation Danielle is hoping to go intoteaching as there is not only a shortage ofmaths teachers but also I know my job will besecure for a long while.


13/24

What difference

do the universitys

research activities

make to me?

Maths is forever changing and growingas more discoveries are made and newapplications for these are found. Manyuniversities are involved in this mathematicalresearch. Many university lecturers combineexpertise and experience in both teachingand research.

In a research-orientated department, thelecturers may be more up-to-date with thelatest developments in their particular subjectand might be world-renowned experts in thefield. In a teaching-focussed department,you may find a higher proportion of staffwhose main interest is in the best ways ofteaching and learning and who may havemore time available to help students. But alllecturing staff should have adequate subjectknowledge andcommitment to teaching tobe able to teach you effectively and to makecourses interesting and relevant.

Research-led universities often usepostgraduate students (postgrads) andpostdoctoral research fellows (postdocs)to help with tutorial teaching and marking.This may result in smaller class sizes.Whilst postgrad and postdoc tutors are lessexperienced, they are often very popular withstudents because they are closer to yourown age and outlook.


14/24


15/24


16/24

What is meant

by pure and

applied at

university? How

theoretical or

practical is a

maths degree?

It is hard to define pure and appliedbecause it changes over time and with thelevel of study. For example, many of thetopics you call pure at A level are treated asapplied maths at university. Prime numbersused to be considered very pure but nowform the basis for much of the cryptographyused, for example, in online banking. Puremaths involves an attempt to understandprecisely why and when methods or ideasare valid and inherent elegance and interestplay a big role. Applied maths looks at waysof using mathematical ideas and methodsin real life; here practicality and usefulnessare desired.

Do I have to

decide whether

Im a pure

or applied

mathematician

or a statistician

before I apply?No. Most universities offer a general mathsdegree (UCAS code: G100) which willusually include pure and applied maths andstatistics in the first year, so you dont needto decide which branch interests you now.A few institutions do offer courses whichspecialise from the start refer to UCAS orthe university prospectus.

Most university courses are modular andyou will build up credits towards your degreeby passing individual modules. In mostuniversities, the majority of your first-yearmodules will be compulsory. By the timeyou reach your final year some universitiesoffer you an enormous choice of modules,allowing you to specialise. Others have amuch smaller choice. If you have specificfuture interests in mind for example ifyou want to study mathematical physics orfinancial maths or statistics to a high level,then you need to ensure that there aresuitable options in the course you choose.A course with lots of options will alsogive you the flexibility to follow your maininterests if these change (as they often do)during your time at university.


17/24

BenjaminAge 21, Final year

BSc Mathematics with

Business Finance

Benjamin always found that maths madesense to him.What I like about maths is that there is eithera right or wrong answer and I dont needanyone to explain it to me; I can work throughthe problem at my own pace. He did a jointhonours course because I wanted to break up

What does a

maths degree

contain?

Only calculus and linear algebra arerequired subjects in every maths degree.You need to look at university websitesand prospectuses or talk to staff to find

out what the course contains but you mayfind the names given to subject areas hardto understand at first. At the end of thisbooklet we give a brief explanation of someof the subjects you might meet in your firstyear at university.

How is technology

used in university

maths?

In any degree you will be expected todevelop your general IT skills, for exampleresearching online and word processing.In addition, on a maths course you mightbe expected to develop specialist skills,for example programming, using statisticssoftware, computer algebra systems orpowerful graphics packages. Attitudes tothe use of technology in maths vary; forexample there are universities where onlybasic calculators (or none) are allowed inexams and others where very powerfulprogrammable calculators or computerscan be used.

VictoriaAge 22,

Graduate,

MMath

Victoria decided tostudy maths at university because shealways appreciated the problem solvingand use of logic it required. She likes thefact that the subject allowed her to learntechniques that had many applications ineveryday life and in other fields. She noticedsome difference between how the subjectis approached at university and how it isapproached at A level, with greater emphasison understanding where concepts have

come from and in learning how to justifyyour own work, and says the course allowedher to study topics in greater depth and tofeel even more confident when applying herknowledge in abstract settings. The coursealso enabled her to develop computerprogramming skills, which are invaluable inmany maths-related careers.

By studying on a Masters in Mathematics(MMath) course she was able to studya wider range of both pure and appliedmodules, with the opportunity to specialise

later in the course.

She says the problem solving, logic andcomputing skills developed while studyingmaths at university are highly soughtafter by many employers and, as a result,studying maths opens up a wide variety ofcareer opportunities. I am now applying theknowledge I have gained by studying for anMPhil in maths and electrical engineering.


18/24

What are maths

classes like?

How big are theclasses?

The style of classes you will encounterdepends on the university and the individualmembers of staff but its usually verydifferent from what you are used to at schoolor sixth form college.

Traditionally, most maths lectures consist ofthe lecturer introducing the material, working

through and explaining both the theory andexamples, with the important details writtenon the board, and students taking notes.

These days, this is just one approach;notes are sometimes given online or inprinted handouts and the lectures are oftenmuch more interactive (meaning youll beexpected to get involved!). Depending onthe size of the department and the particularmodule, classes might have anything from

10 to 300 students in them; bigger classesare less likely to be interactive.

Lectures are usually supported bysmall-group teaching, often called tutorialswhich, depending on the university, couldbe anything from 2 to 30 students. Smallergroups can be taught by postgraduatestudents, postdocs or lecturers, againdepending on the university. The format canvary but might include individual work, group

work, working through exercises at the frontof the class or asking for individual helpfrom the tutor.

You may also find classes where you workon set exercises with a tutor available to help similar to many maths classes at school.

These might be in a traditional classroom or,where appropriate, a computer room. Someuniversities call these tutorials and some callthem exercise or example classes.

In departments with fewer students, thedistinction between lectures, tutorials andexample classes may be blurred, with eachclass containing elements of all of them. Inthis way the teaching might be similar to manymaths classes in school.


What are the compulsory topics and

what are the optional topics? If there

are particular topics or applications

which you are interested in, does

this university offer modules in these

subjects?

What is the course attitude to the use

of technology within maths? Is the use

of technology encouraged throughout

the course or only in specific

modules?

How big are the classes?

How many hours a week of teaching

will I get?What are typical lectures and tutorials

like?

What support is available?

How much is assessed through exams

and how much through coursework?

Will I get the opportunity to do a

personal project in the final year?


19/24

What support is

there when I get

stuck?Everyone gets stuck sometimes so itsworth asking what help is available whenyou do. Some universities encourage you towork with your fellow students and usuallythis is the first place students go for help.Some places organise special sessionswith students from higher years. Some havesmall tutorial groups with members of staffor with postgraduate students. Some have

drop-in sessions where you can go withany maths problems. Some lecturers haveoffice hours when you can call in and askfor help and some have an open-door policyso you can call round at any time. Someuniversities have an online forum wherestudents and sometimes staff help withquestions. Many lecturers will also offersupport via email.

How will I be

assessed?

Again, there are different approaches to assessingyou. Formal examinations are as unavoidable asdeath and taxes wherever you study, but at someuniversities almost all your assessment will bethrough examinations whereas, at others, there canbe substantial credit given to coursework.

Coursework includes a wide variety of tasks:written solutions to mathematical exercises areprobably the most common but you may also beexpected to write reports, do group work, makepresentations or write computer programs. Inmany universities a substantial proportion of yourfinal year might be spent on an individual project,allowing you the opportunity to work on somethingthat particularly interests you at the same time asdeveloping valuable skills for the future.


20/24

Understanding

the syllabus for a

maths degree can

be tricky because

it includes words

and ideas which

may be unfamiliar

to you.

Here we try to give you a flavour of whatyour first year might involve and explainsome of the terms you will meet.

Some of the maths you meet at university isan extension of ideas you have already metduring your previous study. For example,

many courses have a first-year module perhaps called Mathematical Methodsor Techniquesor Calculus designed toconsolidate and build upon topics which,at A level, you treated as pure maths but at

university are considered basic tools for othersubjects. At A level you have probably alreadymet Statisticsas a means of finding thetrends in, and drawing conclusions from, data;at university you will extend these ideas andlearn how to design experiments effectively sothat the data you gather is genuinely useful.

Sometimes the meaning of words you arefamiliar with changes as your study advances.For example, you have met algebra, but atuniversity you will study Linear Algebra,which is the maths of matrices and vectors,how to manipulate them and use them.One important mathematical application isthe solution of large sets of simultaneousequations and some of the ideas in this areahave unexpected practical applications, suchas the technology behind internet searchengines.


21/24

You may also meet Abstract Algebra;for example group theory and ringtheory which look at combinations ofsets (for example, the set of all integers)and operations (for example, additionand multiplication) that satisfy certainconditions.

At school, Geometryis the study of sizeand shape in two or three dimensions but atuniversity similar ideas can be extended, forexample imagining relationships betweenshapes in more than three dimensions.In addition there are some topics whichwill be new to you. For example, Analysisis about what happens when something

becomes infinitely large or infinitesimallysmall. It underpins and extends calculusand also includes the study of infinite seriesand sequences.

0

1

2

-1

-2

0.2

0.3 0.8

0.7

Differential equationsare equations whichcontain derivatives and they are useful todescribe many situations where somethingchanges. These include predictingthe spread of a disease, designingaerodynamic shapes for cars or turbines

and studying aspects of the human body.

Intriguingly, many differential equations(and other mathematical problems) cantbe solved exactly so you may learn aboutNumerical Methodswhich are ways to findapproximate solutions to problems, usuallyusing computers, along with finding out howaccurate the resulting answer is.

Most courses include Modelling, which is

the art of using maths to represent a real-world problem. This involves deciding whatsums to do and, crucially, analysing andcommunicating the results.

Across all your modules, you are likely tofind that Proofplays a much bigger rolethan at school; in other words, how can webe 100% certain that something is true?By understanding the rules of Logicanddeductive reasoning, mathematicians take

pride in understanding exactly what we do and dont know.


22/24


23/24


24/24

Produced by the more maths grads(MMG) project and jointly funded by MMG and the

London Mathematical Society (LMS). MMG is a collaboration between the LMS, theInstitute of Mathematics and its Applications, the Royal Statistical Society, the Heads of

Departments of Mathematical Sciences, and the Maths, Stats & OR Network.Text by the MMG Higher Education Curriculum Team (Mike Robinson, Neil Challis and Mike

Thomlinson) with contributions from many others. Design by James Anthony Graphics

The Institute of Mathematics and its Applications is a charity registered with the Charity Commission, no. 1017777The London Mathematical Society is a charity registered with the Charity Commission, no. 252660

The Royal Statistical Society is a charity registered with the Charity Commission, no. 306096

If you would like to order fur ther copies of this booklet,please visit the mathscareers website - www.mathscareers.org.uk

HoDoMSHeads of Departments of Mathematical Sciences in the UK

Cert no. CU-COC-807950

Des

ign:

info

@

jamesan

thonygrap

hics.c

om

Reor

der:

info

@

pins

tripegroup.

co.

uk-quo

te

41934

Documents

math at uni