Lecturer
Please contact
Dr H. Bruin
for further information about this module.
Announcements
The final test/exam is on Monday February 1st, 5-7pm .
The material is everything on sequences & series,
Class Notes Section 10-16, but excluding Section 13.
On February 1st, there will be a revision class (LTM 10-12am).
Feel free to ask any maths question you like; I will probably go
though exercises and/or tests from a previous year.
Apart from this lecture, the lecture of Tuesday January 12 will be the
last of the semester. In other words: no lecture on Friday January 15.
The hand-out exercise sheet on series, radii and regions of convergence
can be downloaded
here in pdf.
I added solutions, but my advice is of course to first try again, before your consult the solutions, and when you do look at the solutions,
try to follow every step of them.
(Note that there is a typo in the version I handed out on Friday: In
the hint for Question 2(d), the inner sum should range from k=n up to
infinity. This is corrected in the downloadable version.)
A test of previous year, to practice on, here in pdf.
BBC Human domino
A website on
sup/inf/max/min
A website on
Achilles and the Tortoise
Class Details
| Day | Time | Room | Weeks |
|---|
| Tuesday | 2-3pm | LTF | 1-12 |
| Tuesday | 3-4pm | 03MS01 | 1-12 |
| Friday | 3-4pm | LTE | 1-12 |
Assessment
Assesment is based on three class tests:
- Class test 1 (worth 30%) will take place in week 5.
- Class test 2 (worth 30%) will take place in week 9.
- Exam (worth 40%) will take place in week 14 or 15.
All tests are `Closed book': Only pen, pencil, blank scrap paper and pocket calculator
(although you won't need that one) are allowed.
Unassessed Assignments
In addition to the class tests, take-home assignments will be given.
These will be corrected (i.e. feed-back and solutions given) but you
receive no grade for them.
However, they are very important to master the material, and
some class-test question may be drawn directly from them.
The hand-in dates will be in weeks 3, 7 and 11.
Class Test Dates and Coursework Deadlines
-
Unassessed Coursework 1 plus Solutions (in pdf)
Hand-in date: Friday October 23 (in class or at the Undergraduate Office 08AA02).
- Class test 1 (worth 30%) will be on Friday November 6th.
- Unassessed Assignment 2 hand-out date Friday November 13 (in pdf)
Hand-in date: Friday November 20th (in class or at the Undergraduate Office 08AA02).
- Class test 2 (worth 30%) will be on Friday December 4th.
- Unassessed Assignment 3 hand-out date Friday December 11 (in pdf).
Hand-in date: Friday December 18th
(in class or at the Undergraduate Office before 08AA02).
- Class test 3 (worth 40%) will be in January.
Course material (hand-outs/assignments)
-
Class notes available in postscript
and pdf
- A free downloadable (but quite long) text book
Introduction to Real Analysis
by Professor William F. Trench.
-
Exercise sheet for Tuesday October 13
in pdf
-
Exercise sheet for Tuesday October 20 plus template for `proof by induction'
in pdf
-
Hand-out Friday November 3: make your own function octahedron
in pdf.
-
Exercise sheet for Tuesday November 3
in pdf
-
For practice, the first test of 2008 and solutions in
pdf
-
Exercise sheet for Tuesday November 10
in pdf
-
Assignment 2 to be handed in on Friday November 20, in class or in the UG offices before 5pm.
First page first page and
and second page.
The full coursework minus picture plus solutions is
here in pdf.
-
Exercise sheet and hand-out for Tuesday November 17
in pdf
-
The first test (from Friday November 6th) + solution
in pdf.
There were three slightly different test papers, all included in this file.
To spare trees, make sure what yo need before printing.
-
Exercise sheet 6 and hand-out for Tuesday November 24
in pdf
-
For practice, the first test of 2007 and solutions in
pdf.
Note however, that the material of two years ago is not exactly parallel to
the material of this year, so Problem 1 may be a bit too puzzling to you.
-
A proposition on limits of sums, products and quotients of sequences with some excamples. hand-written and scanned in
pdf.
-
Assignment 3
plus solutions here in pdf.
-
Solutions of Test 2 (of December 4th) in pdf.
-
The hand-out exercise sheet of December 18th on series, radii and regions of convergence
can be downloaded
here in pdf.
-
Test 3 + solutions of 2008 (for practice) in pdf.
Selected Texts
-
J. M. Howie, Real Analysis, Springer (2001) 2nd edition,
ISBN 1-85233-314-6
Further texts can be found in the library. For example:
- R.P. Burn, Numbers and Functions, Steps into Analysis,
Second Edition, Cambridge University Press (2000).
- P.E. Kopp, Analysis, Arnold Publishers, (1990).
(Looks more useful for Real Analysis 2)
- K.E. Hirst, Numbers Sequences and Series, Arnold Publishers, (1995).
- C. McGregor, J. Nimmo and W. Stothers, Fundamentals of University Mathematics, Albion Publishers, (1994).
- M. Spivak, Calculus W.A. Benjamin (1967).
- S. Lang, Analysis I Addison-Wesley (1968).
Past examination papers
The assessment of this module is based mainly on class tests,
so there are no
past examination papers available.
