5CCM115B Numbers and Functions for Joint Honours

4CCM115A Numbers and Functions


Semester 1, 2011-2012

Lecturer:      Dr A Pushnitski 


Brief outline of syllabus:

Sets and functions. Real numbers. Sequences, convergence, subsequences, limit points.
4CCM115A is for the 1st year students on: Maths BSc and MSci, Maths with Management and Finance BSc, Maths and Physics BSc and MSci, Maths and Physics with Astrophysics BSc, Maths and Philosophy BA, and Junior Year Abroad (JYA) students.

5CCM115B is for Maths & Computer Science BSc (2nd year students).

Assessment 4CCM115A and CM115A:

There are three tests during the semester, and a fourth test in January, which count for 20% of the final mark. The remaining 80% of the course marks are assessed by a two-hour written examination at the end of the academic year.

Assessment 5CCM115B:

The course is assessed by a three-hour written examination at the end of the academic year.

Course notes:

Notation
1. Sets and functions
2. Logic and proofs
3. Real numbers
4. Sequences: convergence
5. The algebra of limits and the sandwich theorem
6. Standard sequences and rates of convergence
7. Monotone sequences
8. Subsequences and limit points
9. Absolute and conditional convergence of series
10. The limit of a function

Notice board:

Any relevant announcements will be published here


Teaching arrangements:

Three hours of lectures each week, together with a one-hour tutorial. No tutorials in week 1; tutorials start in week 2.

Lectures: Tutorials:

Tutorial groups: times, rooms, tutors

Please note the pop-in tutorials, listed in the website linked above.

Calendar:


Week 1 (starts 26 September): lectures start
Week 2 (starts 3 October): tutorials start
Week 3 (starts 10 October): Assignment 1 collected
Week 4 (starts 17 October): Assignment 2 collected
Week 5 (starts 24 October): Assignment 3 collected
Week 6 (starts 31 October): Assignment 4 collected
7-13 November: reading week, no lectures or tutorials
Week 7 (starts 14 November): Assignment 5 collected
Week 8 (starts 21 November): Assignment 6 collected
Week 9 (starts 28 November): Assignment 7 collected
Week 10 (starts 5 December): Assignment 8 collected
Week 11 (starts 12 December): Assignment 9 collected

Assignments:

Exercise sheets will be placed here on a weekly basis and written answers must be given in to your tutor by the due date.
You are expected to print out these assignments yourself and take them with you to the tutorial.

Assignment 1 (take this with you to the tutorial session during week 2; submit at the tutorial session during week 3) and Solutions 1

Assignment 2 (take this with you to the tutorial session during week 3; submit at the tutorial session during week 4) and Solutions 2

Assignment 3 (take this with you to the tutorial session during week 4; submit at the tutorial session during week 5) and Solutions 3

Assignment 4 (take this with you to the tutorial session during week 5; submit at the tutorial session during week 6) and Solutions 4

Assignment 5 (take this with you to the tutorial session during week 6; submit at the tutorial session during week 7) and Solutions 5

Assignment 6 (take this with you to the tutorial session during week 7; submit at the tutorial session during week 8) and Solutions 6

Assignment 7 (take this with you to the tutorial session during week 8; submit at the tutorial session during week 9) and Solutions 7

Assignment 8 (take this with you to the tutorial session during week 9; submit at the tutorial session during week 10) and Solutions 8

Assignment 9 (take this with you to the tutorial session during week 10; submit at the tutorial session during week 11) and Solutions 9

Assignment 10 (take this with you to the tutorial session during week 11; you will not need to submit this sheet) and Solutions 10

CHRISTMAS CHALLENGE


Class tests (4CCM115A and JYA students only):

Class tests schedule

Books and websites:

There is no set book for the course. However, there are a variety of sources that are useful for certain sections of the course:
  1. Ivan Wilde's Analysis lecture course
  2. The most common errors in undergraduate mathematics - extremely useful and well written website.
  3. K.E.Hirst, Numbers, Sequences and Series (Edward Arnold, 1995)
  4. V.Bryant, Yet Another Introduction to Analysis (Cambridge University Press, 1990)
  5. R.Haggarty, Fundamentals of Mathematical Analysis (Addison-Wesley, 1992)


Exam:

The course is assessed by a two hours exam paper.
In the past, exam length was 3 hours, below is a sample paper.
Summer 2010 Exam paper and solutions


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