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Chris Fenwick

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Xmas and easter test. Optional (you choose) Advanced exam. 20% in total. 8 cswks ... Week before xmas test week. Week before reading week. This week (tomorrow ?) Date ... – PowerPoint PPT presentation

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Title: Chris Fenwick


1
  • Chris Fenwick

2
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

3
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

4
What is maths about ?
What does this mean ?
5
What is maths about ?
What does this mean ?
6
What is maths about ?
What do you think meaningmeans when talking
about maths ?
7
What is maths about ?
Does the following make mathematical sense ?
8
What is maths about ?
Does the following make mathematical sense ?
9
What is maths about ?
Does the following make mathematical sense ?
10
Something more subtle
?
does give
11
Something more subtle
?
does not give
Why ?
12
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.
13
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 !!!
14
  • 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

15
  • Minkowski had urged mathematicians to face
    problems with a minimum of blind calculation, a
    maximum of seeing thought.
  • Hermann Minkowski (1864 - 1909)

16
The maths courses
  • Mathematics is not just about
  • Formulae and rules
  • or solving problems

17
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

18
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.

19
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

20
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

21
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

22
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

23
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.

24
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.

25
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

26
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 !!!

27
The intention of lectures and tutorials
  • Then,
  • tutorials are there to give you time to think
    about, and practice, mathematics

28
The intention of lectures and tutorials
  • So, in a lecture I will say
  • _at_/!/
  • and you hear bla, bla, bla

29
The intention of lectures and tutorials
  • Then, we do a tutorial
  • and you do some private study

30
The intention of lectures and tutorials
  • Now, I say
  • _at_/!/
  • and you say Aaahhhh !

31
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.

32
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

33
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

34
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

35
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

36
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.

37
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.

38
Mathematics groups
  • Topics to be covered in the test are
  • Basic Functions
  • Basic Algebra
  • Basic Trigonometry
  • Basic Differentiation
  • Basic Integration
  • Basic Complex numbers

39
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.

40
Assessments
41
Very important
  • For coursework, tests, exam, etc
  • all steps/working must be shown

42
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

43
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

44
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.

45
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.

46
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

47
Personal behaviour
  • Lateness
  • Please do not be late
  • If you come to a class late you will be
    interrupting all of us

48
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.

49
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 ?

50
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.

51
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

52
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

53
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.

54
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.

55
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 !

56
Some comments
  • So, dont follow us

?
?
57
Some comments
  • Sometimes you might choose to follow us, but
    generally you will make your own path

?
58
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

59
  • The End
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