Chris Fenwick

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• Chris Fenwick

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What will be useful now

• It will be useful if you do not
• Copy anything shown here today
• You will find these slides on my website
• It will be useful if you do
• Listen to todays talk
• so that you can get a sense of what the maths
  course will be about

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What to remember

• The most important thing to remember is ...
• www.ucl.ac.uk/uczlcfe
• Here you will find
• Todays talk
• All the notes for the maths course
• Example tests and exams
• Other stuff

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What is maths about ?
What does this mean ?
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What is maths about ?
What does this mean ?
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What is maths about ?
What do you think meaningmeans when talking
about maths ?
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What is maths about ?
Does the following make mathematical sense ?
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What is maths about ?
Does the following make mathematical sense ?
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What is maths about ?
Does the following make mathematical sense ?
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Something more subtle
?
does give
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Something more subtle
?
does not give
Why ?
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Something more subtle
For ?
The process of integration for areas does exists
because the process of calculating areas is what
integration is.
For ?
There is no such thing as integration which gives
the formula since there is no direct process for
integrating xn.The process is in fact indirect
and comes from differentiation.
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Something more subtle
Controversial ?
Note that this is my opinion, and it is my
opinion.It is based on my experience of maths
and what I think integration means.
Other people may disagree with me !!!
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• Mathematics can be read on several levels, and
  of course some are accessible only to the expert.
  
• But we can always ask, and we should always ask
  What is important about that ? What is
  interesting about that ?
• Jeremy Gray

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• Minkowski had urged mathematicians to face
  problems with a minimum of blind calculation, a
  maximum of seeing thought.
• Hermann Minkowski (1864 - 1909)

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The maths courses

• Mathematics is not just about
• Formulae and rules
• or solving problems

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The maths courses

• Mathematics is about developing experience in
• Understanding concepts and procedures,
  understanding how problems are solved and why
  they are solved in this-or-that way.
• Becoming fluent in the use of these concepts and
  procedures

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The maths courses

• Mathematics is about developing experience in
• Being able to see patterns and generalisations.
• Being able to describe concepts, procedures,
  problems, and how to solve them.

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The maths courses

• Hence the aims of the course are to
• Be able to solve problems
• such as solve x2 ? 1 0
• as well as

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The maths courses

• Hence the aims of the course are to
• think mathematically, for example by finding
  patterns.
• Example find a pattern for the sequence
• 1, , 64

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The maths courses

• Hence the aims of the course are to
• In other words
• 1, 2, 3, 4, , 64
• or 1, 4, 9, 16, , 64
• or 1, 2, 4, 8, , 64
• as well as

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The maths courses

• Hence the aims of the course are to
• Understand the mathematical concepts behind the
  symbols
• In other words ymxc is not
• y equals m times x plus c
• but is
• straight line of slope m, intercept c

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The Lectures

• The aims of the lectures will be to introduce and
  go through the weeks topic
• but I may/will not cover everything presented
  in the notes. You may/will need to do some
  private reading.

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The Lectures

• The aims of the lectures will be to introduce and
  go through the weeks topic
• Lectures are therefore only there to present an
  outline or overview of the topic, not the depth
  or detail of the topic.

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The tutorials

• The aim of the tutorials will be to
• Cover the depth and detail of the topics covered
  in the lecture
• Either by doing some activities together
• or by you spending time revising, doing
  exercises, asking me for help, etc

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The intention of lectures and tutorials

• Note that
• lectures are designed only to provide you with
  an initial overview to the topic
• not to provide a completed understanding for
  you, so that you dont have to do any more
  thinking !!!

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The intention of lectures and tutorials

• Then,
• tutorials are there to give you time to think
  about, and practice, mathematics

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The intention of lectures and tutorials

• So, in a lecture I will say
• _at_/!/
• and you hear bla, bla, bla

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The intention of lectures and tutorials

• Then, we do a tutorial
• and you do some private study

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The intention of lectures and tutorials

• Now, I say
• _at_/!/
• and you say Aaahhhh !

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Your own private study times

• It is important to understand that
• You should not rely totally on the lectures
  /tutorials for your learning of the subject
• you must be more independent in your learning,
  e.g. by doing your own research, reading,
  revision, study, etc
• this is what is expected of all students at
  universities in the UK.

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Your own private study times

• It is important to understand that
• I will not teach every topic in the notes I hand
  out
• but I may set cswk, test and or exam question
  on these topics
• It will be up to you to read the relevant topics
  from then notes and/or books

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Syllabus

• The brief content of the syllabus is
• Pre-requisite knowledge Functions (see my
  website) and trigonometry (see website)
• Algebra
• Differentiation
• Integration
• Complex numbers
• Ordinary Differential Equations
• Series
• Vectors

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Mathematics groups

• Their will be 2 maths groups
• the core group and the advanced group.
• The advanced group will study more topics in more
  depth.
• Which group will you be in ? Sit the filter test

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Filter test

• What There will be a test to decide if you go
  in advanced group or core group
• When This week (tomorrow ?)
• Pass mark There is no pass mark ! The top 100
  students will go into the advanced group, and the
  rest will go in the core group

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Mathematics groups

• Note Do not worry about this test !!!
• This test does not count towards your final
  course mark
• it is only for our information to help us
  decide which group you should go in.

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Mathematics groups

• Do not worry if, when you site the test, you do
  not know how to solve some of the questions.
• This is exactly what the test is there for to
  tell us what you know and what you dont know.

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Mathematics groups

• Topics to be covered in the test are
• Basic Functions
• Basic Algebra
• Basic Trigonometry
• Basic Differentiation
• Basic Integration
• Basic Complex numbers

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Core Textbooks

• There is no one maths textbook which will cover
  our topics to the necessary depth and detail !
• Use the math books in the SAC, as well as the
  main library.

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Assessments
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Very important

• For coursework, tests, exam, etc
• all steps/working must be shown

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Show all steps/working

• In any work you do only 5-10 (or less) of your
  marks comes from getting the correct answer !!!
• 90 - 95 (or more) of your marks comes from
  showing all the steps needed to get the answer

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Assessments

• All cswks, all cswks, are individual pieces of
  work
• The work you present in your cswk must be your
  own work.
• You must not copy any work from friends, books,
  internet etc

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Assessments

• But this does not mean you cannot work together
  
• all it means is that you must present your own
  method of solution, not your friends method of
  solution.

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Personal behaviour

• Talking in class
• It is very distracting to everyone if you keep
  talking in class.
• So please keep talking to a minimum
• and only whisper.

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Personal behaviour

• Lateness
• Lectures are not drop-in sessions
• in other words you cannot arrive to lectures
  when you feel like it.
• Lectures will start on time, therefore

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Personal behaviour

• Lateness
• Please do not be late
• If you come to a class late you will be
  interrupting all of us

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Personal behaviour

• My Office
• I share an office with several other people
• Our office is not an open access office
• you cannot just walk into our office
  unannounced, so
• Please knock and wait until someone calls you in.

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Some comments

• A question
• Do I know everything about mathematics ?
• Answer No
• Do I know everything about the mathematics of the
  course I will teach you ?
• Answer No !!! Why ?

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Some comments

• I do not know everything about maths !!
• You may see connections which I did not see
• or you may talk of an idea which I had not
  thought of.
• Therefore I may not be able to answer your
  question straight away. I might need time to
  check it out.

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Some comments

• I do not know everything about maths !!
• or you check it out yourself !
• A major part of learning at university is based
  on independent reading, study, learning etc...
• NOT on you always waiting for the lecturer to
  give you the answer to everything or
  solve/explain/tell you everything

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Some comments

• about teaching the subject of maths
• The course is about maths
• not about tests/exams/cswks !
• Hence we are here to teach maths
• we do not teach because there are test or exams
  to pass

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Some comments

• about marks / grades
• We are here to help you learn. We are not here to
  give you marks.
• The mark that you get is the mark that YOU get
  for the quality of the work YOU have done.

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Some comments

• about marks / grades
• Come and talk to us about your work and how you
  can improve it, NOT about the mark you got
• or the mark you wanted but didnt get.

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Some comments

• Finally
• Do not let us stop you from learning more
  advanced maths if you want to,
• do not let yourself be held back by us or the
  syllabus !

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Some comments

• So, dont follow us

?
?
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Some comments

• Sometimes you might choose to follow us, but
  generally you will make your own path

?
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What to remember

• The most important thing to remember is ...
• www.ucl.ac.uk/uczlcfe
• Here you will find
• Todays talk
• All the notes for the maths course
• Example tests and exams
• Other stuff

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• The End