Analysis 1 2013-14

Timetable: Lectures Mon 10, Fri 3; in Tyndall LT, Physics.
Problem Classes this semester: Jan 29, Feb 12, 19, Mar 5
, 19, April 2; in Chemistry LT1.

Lecturer: Dr Misha Rudnev. Office 2:10 Howard H. Office Hour Mon 11-12 or by appt.



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: nm 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.

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