Official Unit
description
Tim
Gowers (a great mathematician) blog on what an analysis proof is like
Course materials:
Lecture
Notes (If
you see any typos, etc., please, e-mail me.) May undergo
a little editing as we progress.
Typos list (thank you, get me more!):
P. 36, after Def 2.4.2: b = inf S should read a = inf
S.
P. 38, the fourth line of the proof of Theorem 2.4.3: n≤m should read n≥m.
Slides
for selected lectures
Links. (This material is meant to be known from
school, and is not part of the Notes. But for general Maths foundaitons
at least doing the arithmetics in base 2, other than base 10 is
important. There will be allusions to base 2 and possibly base 3
representation of real numbers in the FTA course. So here is some nice
and easy reading, which is mandatory if you are not comfortable with
arithmetics with bases other than 10.)
Representation
of integers with various bases,
Representing
rationals using various integer bases
As a matter of fact, if you find the above too wordy, here
is a compendium of what you should know about integers
and rationals expressed in different bases
Exercise sets:
1
2
3
4
5
6
7
8
9
10 11
12
13 14 15
16
Solutions to Exercise sets:
1
2
3
4
5
6
7
8
9 10
11
12
13
14
15
16
Weekly homework (assigned
on Wednesdays, due the following week):
Week 1: Sheet 1, Exercises 2-5.
Week 2: Sheet 1, Exercises 6(b), 7, 10, 12, 13, 14, 16.
Week 3: Sheet 2, Exercises 1(b), 2(a), 3(b,d,f), 5(c,d), 6(c,e),
7(a), 8.
Week 4: Sheet 3, Exercises 1-5, 7.
Week 5: Sheet 3, Exercises 8(b,c), 10(a), 11, 12(a,c). Sheet 4,
Exercises 1,4.
Week 6: Sheet 4, Exercises 7, 8, 9, 11(a,c), 12, 13.
Week 7: Sheet 5, Exercises 2, 3, 5(a), 6.
Week 8: Sheet 5, Exercises 7-10. Sheet 6, Exercises 1-3, 4(d).
Week 9: Sheet 7, Exercises 1(a,b,e), 2, 5, 7, 8, 9.
Week 10: Sheet 8, Exercises 1, 2, 3, 4(a,b), 5, 6.
Week 11: Sheet 8, Exercises 7, 8(a,b,d-f).
Week 12: Sheet 9, Exercises 1, 2, 3(a-c).
Week 13: Sheet 9, Exercises 3(d,e), 4,5.
Week 14: Sheet 10, Exercises 1, 2 (ii), 3, 4.
Week 15: Sheet 11, Exercises 1, 2, 3, 5(a,c), 8, 9.
Week 16: Sheet 12, Exercises 1, 2(a), 4, 5, 8, 9,10.
Week 17: Sheet 13, Exercises 1, 2, 4, 5, 6.
Week 18: Sheet 13, Exercises 7, 9, 10, 12; Sheet 14, Ex. 1.
Week 19: Sheet 14, Exercises 2(a,c), 3, 4, 6(a,b), 7(a).
Sheet 15, Ex 3.
Week 20: Sheet 15, Exercises 1, 4, 6.
Week 21: Sheet 15, Exercises 5, 7, 8, 9(a), 11.
Week 22: Sheet 16, Exercises 1, 2, 4, 5, 7, 10. (due the first week after the break).
Recommended
textbooks:
Past examination
papers:
here is a link, tiles are self-explanatory
click
here.
They are also available for download on Blackboard.
Go to My Home Page |