ACCELERATED PROOFS AND PROBLEM SOLVING
COURSE STRUCTURE
1. Basic facts
This course is an accelerated version of Proofs and Problem Solving course, intended principally for students on the accelerated programme (direct entry to year 2)
and students on combined degrees who cannot take that course in their first year.
The syllabus is similar to that for Proofs and Problem Solving, but some topics less
essential to further study are omitted or treated more quickly.
• The first lecture will be on Monday 21st September 2015 at 10:00am at room
5326 at James Clerk Maxwell Building (JCMB).
• The first tutorial will be on Tuesday 29th September 2015 at 11:10am at
room 4325C at JCMB.
• The first homework will be set on Thursday 24th September 2015 via Learn
and is due the following Thursday 1st October 2015 in the morning lecture.
Please see the description and the syllabus of Accelerated Proofs and Problem
Solving course at http://www.drps.ed.ac.uk/15-16/dpt/cxmath08071.htm.
2. Timetable
The timetable for week n ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} of Semester 1 is given by
the following table:
Monday
10:00-10:50
lecture 2n − 1
at 5326 JCMB
Tuesday
Wednesday
11:10-12:00
tutorial n − 1
at 4325C JCMB
marked assignments
for week n − 1 are
returned to students
slides for
tutorial solutions
lecture 2n − 1 are for week n − 1 are
posted on Learn
posted on Learn
tutorial problems
for week n are
posted on Learn
Thursday
Friday
10:00-10:50
lecture 2n
at 5326 JCMB
slides for
lecture 2n are
posted on Learn
homework due
assignments
from week n − 1
for week n − 1
during lecture 2n
are marked
homework
for week n is
posted on Learn
homework solutions
for week n − 1 are
posted on Learn
So, the last tutorial will be on Tuesday 1st December 2015, the last lecture will be
on Thursday 3rd December 2015, and the last homework is due on the last lecture.
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3. Lectures
In lectures we will focus on improving your conceptual understanding of the material. The lecture will follow the book A Concise Introduction to Pure Mathematics
by Martin Liebeck (3rd Ed. 2011, CRC Press). Here is a rough guide for how the
chapters will be divided up:
Week
1
2
3
4
5
6
7
8
9
10
11
Chapters
1 and 2
Material
Sets, proofs, quantifiers,
real numbers, rationals and irrationals
3, 4 and 5
Decimals, inequalities,
roots and powers
6 and 7
Complex numbers, roots of unity,
complex and real polynomial equations,
Fundamental Theorem of Algebra
8 and 9
Induction and its applications, prime numbers,
prime factorization, plane graphs,
convex polyhedra, Eulers formula
10, 11 and 12
Euclidean algorithm, prime factorization,
Fundamental Theorem of Arithmetics,
Diophantine equations
13, 14 and 15
Congruence, modular arithmetic,
Fermat’s theorem, congruence equations
16 and 17
Counting and choosing, binomial coefficients,
multinomial coefficients, set theory
18 and 19
Equivalence relations, functions,
injections, surjections, bijections
20
Permutations, cycles, parity,
ghosts of Group Theory
22 and 23
Countable and uncountable sets ,
sequences and their limits
21 and 24
Bounds and real numbers,
continues functions and their properties,
Intermediate Value theorem
4. Tutorials
This course is called Accelerated Proofs and Problem Solving. The problem solving plays crucial role in this course. Keeping this in mind, tutorial attendance is
probably more important than lectures.
You will have weekly tutorials on Tuesdays. It will be very helpful for for you
to do a little preparation before each tutorial. In addition to having gone through
the course material before the tutorial, you should look over the tutorial problems,
which will be posted up on Learn the previous Tuesday. Solutions to these problems
will appear on the Tuesday after the tutorial, but it is not recommended to look at
them until you have seriously attempted the problems!
Almost all tutorial problems will be from the textbook [1]. Solving tutorial problems is very crucial for the exam.
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5. Homework
Each homework assignment will consist of even-numbered questions from the
course textbook [1] (with very few exceptions), of which 5 will be marked each
week by tutors and will count towards the final grade. 15% of the final grade for
the course will come from these problems (taking the best 8 out of 10 assignments).
Homework is set on Thursday via Learn and is due the following Thursday in the
morning lecture. Solving homework problems is very crucial for the exam.
6. Exam
There will be a 2-hour examination during the December 2015 exam diet which
will count 85% to the assessment of the course. This will be an open-book exam: you
may take in a copy of the course textbook and your notes, but no other books. You
are also allowed a calculator from the College approved list. To pass the course you
must achieve an average of more than 40% AND at least 40% in the examination.
If you fail, you may re-sit the examination during the re-sit period in August 2016.
Coursework cannot be re-sat or re-submitted.
The exam problems will be similar to the tutorial problems and/or homework
assignments. They will be based on topics from [1]. The following topics will not
be examined:
• solution of cubic equations described (pages 50-51 in [1]),
• Euler’s formula and Platonic solids (the whole [1, Chapter 9]),
• secret codes (the whole [1, Chapter 15]),
• multinomial coefficients (pages 134-137 in [1]),
• upper and lower bounds (the whole [1, Chapter 22]),
• limits (the whole [1, Chapter 23]),
• continuity (the whole [1, Chapter 24]).
7. Stuff
Course lecturer is Ivan (Vanya) Cheltsov. His phone number is 0131-650-5060. His
email is I.Cheltsov@ed.ac.uk. His web page is http://www.maths.ed.ac.uk/cheltsov.
Please contact him if you have any questions about lectures, homework or tutorials.
Course secretary is Martin Delaney.
His phone number is 0131650-6427.
His email is Martin.Delaney@ed.ac.uk.
His web page is
http://www.maths.ed.ac.uk/people/show?person=90. Please contact him if you
have any questions about the administration of the course.
There will be two tutors for this course: Carmen Li and Sjoerd Beentjes. Carmen
is a Ph.D. student. Her email is k.k.li@sms.ed.ac.uk. Sjoerd is also a Ph.D. student.
His email is s1460452@sms.ed.ac.uk.
Look on Learn for more information about the course and for any announcements.
References
[1] M. Liebeck, A concise introduction to pure mathematics
Third edition (2010), CRC Press
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