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Mathematics: Study skills

Study skills @ Mathematics

Studying at university involves building on your existing skills and developing new ones. Your department librarian is here to support you with your studies and this following page covers some of the essential skills you need to develop. If you would like to book a one-to-one session for advice please drop us an email.

For more in-depth study skills help check out the Study Skills Hub on the Physical Science Guide.

Time management

1. Think about how you currently spend your time

As you work through your tasks make a note of what you find easy, what you find harder, any distractions you might face and how you dealt with them. It also helps to think about any particular times of day when you feel especially productive. Some of us work better in the mornings, others work well later at night whilst for some it doesn't seem to matter. Although it's not always possible to work at your preferred times, knowing when they are can help you to better plan your schedule.

2. Set your priorities

Once you know how you are currently spending your time you can start to solve any problems and capitalise on what is working well. Having multiple tasks on your to-do list can seem overwhelming but the key is to set priorities so that you work on the most important things first. There are several techniques you can use to do this but one of the best is the Eisenhower Method. Named after the US president it allows you to divide your tasks into four groups to see which you need to work on first. If a tasks is important and urgent then it goes to the top of the pile. If you are interested in this technique you can read more about the Eisenhower Method on the Product Plan website. 

Eisenhower Matrix

3. Write a to-do list

To-do lists have come a long way since they were scribbled on the back of envelopes. Writing a to-do list helps you to remember what you need to do and gives you a sense of achievement when you are dealing complete a task. You can of course rely on the traditional pen and paper but there are lots of list and project management apps available which mean you can take your list anywhere you're working. Trello, ToDoist,  and are all easy to use and don't forget that you have access to Office 365 through the University so you could also use Microsoft ToDo. Our top tip: make 'write to-do list' your first entry. That way you can cross something off straight away!

4. Set SMART goals

Once you know what which order you need to tackle your tasks in it's time to set yourself some goals. SMART goals follow the formula below and turn a vague goal such as 'write essay' into something you will actually be able to do.

S - Specific

M - Measurable

A - Achievable

R -Realistic

T - Timely

By making your goals SMART you can develop a plan to follow rather than just trying to finish something. You can read more about SMART goals and time management on the MindTools website.

Mathematical writing

Title page of A Brief Guide to Mathematical Writing by Dr Gareth Wilkes.As well as learning about mathematical concepts and how to apply them you will need to develop a way to communicate your ideas. Formal mathematical writing is likely to be different to what you have experienced before and is an important skill to develop. Your writing needs to be academically sound as well as a good piece of work in its own right. This is what your supervisors and examiners will expect to see during your studies and if you go on to pursue an academic career your colleagues will expect the same.

Dr Gareth Wilkes from the Department of Pure Mathematics and Mathematical Statistics and Jesus College has put together an excellent introduction to mathematical writing. Aimed at first-year students, the guide offers tips and techniques to get you started as you develop your own voice and can be downloaded at the link below.

Study Skills in Mathematics

The Faculty also provides a concise guide to mathematics study skills which is available via the main Faculty website or the link below.

Taking good notes

The important thing to remember about notes is that they are designed as a way for you to remember and react to the key points of a lecture, reading or other source. As long as the system you use works for you the it doesn't matter which one you like. You may find that you end up using different methods depending on the topic or assignment you are working on so it's always good to have a range of methods in your toolkit.

Note-taking methods

Example of the Cornell MethodThe Cornell Method is one of the most popular techniques for recording academic notes. This template offer space for you to record your main thoughts on a topic or reading but also prompts you for some extra information. You can record the title, author and page numbers of what you're reading - vital when it comes to good referencing. There is space at the side of the page for you to note down any keyword, thoughts and questions about a topic which can help you start to think more about what you are reading and how it connects with other ideas. Finally there is space at the bottom of the page to summarise your reading in your own words. Find out more about the Cornell Method.

You can read a summary of the pros and cons of these and other methods on the LifeHack website.

Outline MethodThe Outline Method involves thinking about the main points of a reading and using these as headers to make further notes. Under each of these main headings you can record as many sub-headings as needed followed by any evidence which backs this up or thoughts you have about the material. This method requires you to think about the main topics in your reading and may work best after you have already read through the material once to get an idea of what is being said. The main advantage of this method is that it makes it simple to determine the main points of the reading which is useful for quick revision of a topic. Find out more about the Outline Method.

You can read a summary of the pros and cons of these and other methods on the LifeHack website.

Mind mappingMind mapping is a great way to explore connections. It's also useful if you respond to more visual methods rather than lots of text. Sometimes referred to as spider diagrams, mind maps put a topic at the centre and then draw branches to sub-topics. These can be further divided into more sub-topics and so on. Limited space means that this type of note-taking won't be as detailed but this can stop the problem of just copying down what you have read. The main advantage to this method is that it is easy to draw connections between ideas to help you build up a picture of current thinking. This is especially useful if you're doing any type of literature review. Find out more about mind mapping.

You can read a summary of the pros and cons of these and other methods on the LifeHack website.

Revision and exams

No matter how many exams you've taken so far in your academic career, anxiety about the process is completely normal. This may be the first time you're sitting exams at university and this will inevitably feel different to your previous experiences. The revision process for university level exams is also likely to be different. In the same way that much of your learning at this level will be self-directed, you will have to take more responsibility for your revision.

Remember that undergraduate mathematics exams in Cambridge are non-modular - questions on different lecture topics are spread over each of the four papers. This may impact what and how you choose to revise.

Revision strategies

One of the most obvious places to start your revision is your own notes. Over the course of your studies you will have made notes from a variety of sources including lecturers, supervisions and your own reading. Now is the time to bring all of these together in your revision toolkit.

  • Condense your notes down to the key points that you need to focus on. Record facts, figures and the main arguments in the area. You can start this process by reviewing your notes but as you get further into your revision you might want to see how much you can do from memory. This process can also help to show you were you have gaps in your notes that you need to address. 
  • Always write notes in your own words unless you are recording a direct quote. This can help you to avoid accidental plagiarism but it also helps you to understand the concepts you are writing about. If you find you have copied a lot of your notes you can take the opportunity to rewrite things in your own words to test your understanding. 
  • You can also annotate your existing notes. What have you learnt more about since you took them, where can you see connections and what do you need to know more about? Using a template such as the Cornell Method can help with this as it offers space for annotations and extra notes.
  • Be creative. Use coloured highlighters to pick out the main points or write using different colour pens. This can help your notes to have visual appeal and start to draw connections between topics. Whichever technique you use be consistent - you're trying to make your revision easier not more complex!

Reading your notes or other materials is one strategy for revision but it can also be quite a passive activity. Active reading techniques help you engage with the material which aids processing and retention of the information.

  • A good first step is to determine whether the material is actually worth reading as part of your revision. You will be under pressure to get through as much revision as you can and it's important to stay focused. Use the headings in an article or chapter to assess whether it's on topic and useful to you. You can also take a glance at the contents page of a book or do a keyword search in an online article to look for relevant content.
  • Think about where you can draw connections between this reading and other materials you have read. Make notes in the margins to highlight these connections and pull out any themes.
  • Try and highlight any evidence presented to back up claims made in the material. Consider what you think of this evidence and how it is related to other things you might have read.
  • Test your understanding of what you are reading as you study. Try reading for 20 minutes and then putting the material to one side and noting down the key points without referring back. This will also help you to determine where you need to spend more time reading.

It can sometimes help to translate your notes into a different format. Not only does this make them more visually appealing but the act of transferring your notes can help them to stick in your memory.

  • One of the most simple visual techniques is to keep your notes visible. Write a short list of key points on the topic you are revising and put them somewhere you will keep seeing them - the side of your laptop monitor, the bathroom mirror or above the kettle.  
  • Create a mind map to show connections between ideas and concepts. Sometimes called spider diagrams, these maps start with a main topic in the centre and then branch out into headings and sub-headings. They can be particularly useful if your topic is complex with lots of interconnecting areas and you need to get an overview. You can draw these diagrams yourself on paper or use one of the many apps available to help you create one.
  • Use sticky notes to create a moveable outline of your topic. Use one note per sub-topic and attach them to a surface like a wall or table to create a map. Unlike a mind map you can easily reposition these notes as needed.
  • If you're feeling artistic you can use sketch notes. These visual notes combine words and images to create visually appealing notes. As well as looking good, this process helps you to think about the information in a new way and remember key concepts.

Although a deep understanding of the material is crucial to exam success, sometimes you just need to remember facts or theories. Re-reading your notes or rewatching recorded lectures can help but why not try some of the techniques below?

  • Use mnemonics to help you remember strings of information. These are memory aids with a phrase where the first letter of each word represents the word you want to remember - for example the phrase Naughty Elephants Squirt Water can help you to remember the order of points on a compass. You can use existing mnemonics or make up your own, whatever helps to jog your memory.
  • Tell yourself a story. Revision stories help you to think about information in another way and it's often easier to remember a narrative than a string of facts. Imagine that you want to remember a set of theories and how they interact with each other and what might happen. Think of a story where each theory is represented by students in a class or passengers on a train. Thinking about information in this way will help your recall in an exam situation. 
  • Have you ever found that you seem to know the lyrics to songs without actively trying to remember them? We subconsciously absorb information and you can use the same technique in your revision. Try recording yourself reading your notes and listen to them like a podcast. Repetitive listening whilst doing every day tasks can help you to remember the information.

Looking at past papers in your subject helps you to familiarise yourself with the format of the exam and gives you a chance to complete model answers as a revision tool.

  • Use past papers to test your knowledge at the end of a revision session. You don't have to write a complete answer, just note down the points you would cover to test your recall. You can find a selection of links to past papers in physical sciences on this guide. 
  • Try completing the past paper in a timed scenario. This will allow you get used to exam conditions and help you to plan your time ahead of the big day.
  • Go through your answers afterwards and give yourself a mark. Try to be honest in your assessment. If you can get hold of the grading system used in the actual exam this will be a useful guide to demonstrate where you need to improve.
  • Practice question types that you struggle with. This will give you a chance to get used to the format and identify any gaps in your knowledge you need to address. For example, if you struggle with essay questions then past papers give you the change to develop your strategy.
  • Although very occasionally exams contain questions that have been asked before, memorising answers is not the aim of this revision technique. The point is to use them to test your knowledge and become familiar with the language used. If you try to commit answers to memory you run the risk of answering the question you think is being asked rather than the one that is actually on your paper.

Revision can be a lonely activity but it doesn't have to be. There are lots of ways you can get together with friends to do effective revision and offer each other some moral support.

  • Forming a study group can help you to stay on track with your revision. You can share revision tips and keep each other motivated but it can also be a really useful way to gain a deeper understanding of a topic. Everyone will bring different interpretations and knowledge to their studies and learning about these can help you to get a new perspective on topics.
  • Do a quick fire quiz on core topics, taking turns to ask each other questions. You can use ready prepared flashcards for this or just ask questions at random. This is especially useful to test your recall of key facts and figures that you might need to use in an exam. It's important to vary the order of the questions you ask or you run the risk of just learning the order rather than the actual answer!
  • Try teaching your topic to a friend or a group. Explaining the concepts to them will help test your understanding and how you can communicate beyond listing facts. You might find this method especially useful if you struggle to articulate a response in writing as it offers a different way to revise. If you find long explanations challenging try the 'Just a Minute' format where you have 60 seconds to talk about your topic with no hesitation or repetition. 
  • As with individual revision it's important to build in breaks but make sure that you don't get sidetracked by conversations with your study group too much. 

Past exam papers

Looking through past exam papers can help to familiarise you with the format of the exam and any instructions as well as giving you a chance to draft practice answers. If you want to get the full experience you can answer the questions yourself under simulated exam conditions. You can find past papers for Part IA, IB and Part II on the Faculty webpages.


Self-care is an important part of your study routine. Taking regular breaks, creating a good environment and looking after your physical and mental health can all help to ensure that you get the most out of the time you spend studying.

It's vital to build regular breaks into your study routine to reduce your stress, boost your energy and improve your memory. Most people can only truly concentrate on a task for between 10 and 50 minutes and research has shown that working in short blocks of time with breaks in between is one of the best ways to achieve your overall goal. The Pomodoro Technique encourages us to work in 25 minute bursts to break up a study session.  How long you want to work between breaks will depend on both your project and your individual preferences but why not try some of the ideas below to give yourself a rest.

  • Move to another space. Changing location during your break time can help you to mentally disconnect from your studying and actually enjoy some downtime without getting tempted back to work too soon.
  • Grab a drink or a snack. It's important to stay hydrated to aid concentration and it can be easy to forget to top up your water bottle if you're engrossed in studying. Many people also swear by brain food to help them study - it's hard to concentrate if your tummy is rumbling.
  • Try some gentle exercise. Bupa recommends a series of stretches you can do at your desk if getting up to move around isn't possible where you are.
  • Listen to some music. Your favourite tunes can help to relax you or get you energised for more studying. Check out our science themed playlist on Spotify for inspiration.
  • Try another form of mental stimulation. We know how popular our collection of library jigsaws are and so to replace these, we have created a number of online jigsaws of our own library spaces that you can play during your breaks between study.
  • Read. This might be the last thing you feel like doing but if you've been reading on a screen why not take a break with a paper novel? If you're at the Moore you can check out our Literature Collection on the ground floor.

If you're feeling overwhelmed there are lots of ways to get help. The University offers a range of advice and support services who can help you in confidence and without judgement.

  • Student Wellbeing. These pages contain information on sources of confidential support for all students.
  • University Counselling Service. This service offers confidential counselling and self-directed help guides.
  • Nightline. Chat to someone via text or phone in confidence and without judgement from 7pm-7am.

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