- NUMBERS (MA10001): PROBLEM SHEET 8, SOLUTIONS 1. Write the following complex numbers in the form x + iy
- NUMBERS (MA10001): PROBLEM SHEET 8 Hand in your solutions to questions 1, 2 and 3 to your tutors by 9:00 on Tuesday, 9th
- NUMBERS (MA10001): PROBLEM SHEET 4, SOLUTIONS 1. If n 8 and the coefficients of x7
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 2, SOLUTIONS 1. Let V = (y 2 = x 3 + x 2 ) # A 2 . Is the ``map'' #: A 1 ### V given by t ## (t 2
- INTRODUCTION TO TOPOLOGY (MA30055) PROBLEM SHEET 4: SOLUTIONS
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- INTRODUCTION TO TOPOLOGY (MA30055) PROBLEM SHEET 3: SOLUTIONS
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- NUMBERS (MA10001): PROBLEM SHEET 5 Hand in your solutions to questions 1, 2 and 4 to your tutors by 09:00 on Tuesday, 11th
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- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 5 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
- NUMBERS (MA10001): PROBLEM SHEET 6, SOLUTIONS 1. In each of the following cases, find polynomials M(t) and R(t) in Q[t] with deg R(t) <
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- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 1 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
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- NUMBERS (MA10001): PROBLEM SHEET 2, SOLUTIONS 1. Prove by induction (and not by any other methods you may know)
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 4 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to me at
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 3 Largely a revision sheet. I will look at any solutions you hand in, and return them to you
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- University of Bath DEPARTMENT OF MATHEMATICAL SCIENCES
- NUMBERS (MA10001): PROBLEM SHEET 7, SOLUTIONS 1. Write the following complex numbers in the form x + iy
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 4
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 6 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to me
- METRIC SPACES (MATH0041): PROBLEM SHEET 3 1. Show that if (a n ) is a sequence in a metric space with the property that every subse-
- METRIC SPACES (MATH0041): PROBLEM SHEET 5, Solutions 1. : any will do since d Y (f(x); f(y)) = d Y (p; p) = 0 whatever x and y are.
- METRIC SPACES (MATH0041): PROBLEM SHEET 1, Solutions 1. a) No: 1.1(b) fails because d((0; 1); (1; 1)) = 0
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 2 I will look at any solutions you hand in, and return them to you in due course.
- Toric Fano Varieties and Convex Polytopes
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- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 3 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to me at
- NUMBERS (MA10001): PROBLEM SHEET 8 Hand in your solutions to questions 1, 2 and 3 to your tutors by 9:00 on Tuesday, 9th
- NUMBERS (MA10001): PROBLEM SHEET 5, SOLUTIONS 1. Using Euclid's algorithm, calculate the greatest common divisor d = hcf(a, b) in each
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- NUMBERS (MA10001): PROBLEM SHEET 2 Hand in your solutions to questions 1, 2 and 4 to your tutors by 09:00 on Tuesday, 21st
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 1 I will look at any solutions you hand in, and return them to you in due course.
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 6 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to me
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 1, SOLUTIONS 1. Describe in a few words the affine variety in k2
- NUMBERS (MA10001): PROBLEM SHEET 3 Hand in your solutions to questions 1, 2 and 3 to your tutors by 09:00 on Tuesday, 28th
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- METRIC SPACES (MATH0041): PROBLEM SHEET 6, Solutions 1. i) X = C (usual metric); a n = e in . Bounded as ja n j 1. Not Cauchy or convergent as
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- On some lattice computations related to moduli A. Peterson and G.K. Sankaran, with an appendix by V. Gritsenko
- Smooth rationally connected threefolds contain all smooth curves
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- The moduli space of etale double covers of genus 5 curves is unirational
- Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type
- The Hirzebruch-Mumford volume for the orthogonal group and applications
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- NUMBERS (MA10001): PROBLEM SHEET 2 Hand in your solutions to questions 1, 2 and 4 to your tutors by 09:00 on Tuesday, 21st
- NUMBERS (MA10001): PROBLEM SHEET 6 Hand in your solutions to questions 1, 3 and 4 to your tutors by 09:00 on Tuesday, 218th
- NUMBERS (MA10001): PROBLEM SHEET 7 Hand in your solutions to questions 1, 2, and 4 to your tutors by 09:00 on Tuesday, 2nd
- NUMBERS (MA10001): PROBLEM SHEET 1, SOLUTIONS 1. For each of the following statements, say whether you think it is true or false, and why.
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- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 7
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 8
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- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 1
- FURTHER MATHEMATICAL TECHNIQUES (MA10193) EXAMPLES SHEET 2
- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 1: SOLUTIONS
- MATHEMATICS 2 (MA10193) ASSESSED COURSEWORK
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 2 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 4 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to me at
- INTRODUCTION TO TOPOLOGY (MA30055) PROBLEM SHEET 2: SOLUTIONS
- INTRODUCTION TO TOPOLOGY (MA30055) PROBLEM SHEET 5: SOLUTIONS
- INTRODUCTION TO TOPOLOGY (MA30055) PROBLEM SHEET 6: SOLUTIONS
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 3 Largely a revision sheet. I will look at any solutions you hand in, and return them to you
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 4 I will look at any solutions you hand in, and return them to you in due course.
- Algebraic geometry MA4A5 Homework on Chapter 1
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 2, SOLUTIONS 1. Let V = (y2
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 3, SOLUTIONS 1. Prove that any variety V An
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- ALGEBRAIC CURVES (MA30188): 2003 EXAM Retyped hastily after the original was lost. No guarantees, and no solutions either.
- University of Bath DEPARTMENT OF MATHEMATICAL SCIENCES
- University of Bath DEPARTMENT OF MATHEMATICAL SCIENCES
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- NUMBERS (MA10001): PROBLEM SHEET 6, SOLUTIONS 1. In each of the following cases, find polynomials M(t) and R(t) in Q[t] with deg R(t) <
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 4, SOLUTIONS 1. Find the points at infinity in P 2 of the irreducible curves whose equations in A 2 are
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 4 I will look at any solutions you hand in, and return them to you in due course.
- Boundedness for surfaces in weighted P 4 L.V. Rammea & G.K. Sankaran
- NUMBERS (MA10001): PROBLEM SHEET 7, SOLUTIONS 1. Write the following complex numbers in the form x + iy
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- NUMBERS (MA10001): PROBLEM SHEET 3, SOLUTIONS 1. For each n N, find a formula for
- NUMBERS (MA10001): PROBLEM SHEET 5, SOLUTIONS 1. Using Euclid's algorithm, calculate the greatest common divisor d = hcf(a, b) in each
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- METRIC SPACES (MATH0041): PROBLEM SHEET 2 Reminder: I will mark any work you hand in to me.
- NUMBERS (MA10001): PROBLEM SHEET 6 Hand in your solutions to questions 1, 3 and 4 to your tutors by 09:00 on Tuesday, 218th
- Brief Notes on Metric Spaces, MATH0041 1. Metrics and Norms
- University of Bath DEPARTMENT OF MATHEMATICAL SCIENCES
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- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 1 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
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- NUMBERS (MA10001): PROBLEM SHEET 8, SOLUTIONS 1. Write the following complex numbers in the form x + iy
- NUMBERS (MA10001): PROBLEM SHEET 3, SOLUTIONS 1. For each n # N, find a formula for
- Dimer models and CalabiYau submitted by
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- METRIC SPACES (MATH0041): PROBLEM SHEET 1 1. In each of the following cases, say whether (X, d) is a metric space or not.*
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- METRIC SPACES (MATH0041): PROBLEM SHEET 7, Solutions 1. i) Not compact as it's not closed, and not connected as it is the union of t*
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- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 5 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 3, SOLUTIONS 1. Prove that any variety V # A n has a unique decomposition as V = V 1 # # VN , with
- NUMBERS (MA10001): PROBLEM SHEET 5 Hand in your solutions to questions 1, 2 and 4 to your tutors by 09:00 on Tuesday, 11th
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- Any smooth toric threefold contains all curves G.K. Sankaran
- NUMBERS (MA10001): REVISION SHEET, SOLUTIONS 1. Prove the following statements by induction
- On the degenerations of (1,7)-polarised abelian surfaces
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- FOUNDATION MATHEMATICS I (MATH0103): PROBLEM SHEET 2 Please hand in solutions to the following questions on Monday 16th October. There are
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- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 1, SOLUTIONS 1. Describe in a few words the a#ne variety in k 2 (assume k = R if you like) given by
- Moduli of K3 Surfaces and Irreducible Symplectic V. Gritsenko, K. Hulek and G.K. Sankaran
- METRIC SPACES (MATH0041): PROBLEM SHEET 3, Solutions 1. Suppose an does not tend to a. Then 9ffl > 0 8N 2 N 9n > N d(an, a) > ffl. C*
- METRIC SPACES (MATH0041): REVISION SHEET 1, Solutions 1. The closure W~ of W in X is
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- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 6, SOLUTIONS
- METRIC SPACES (MATH0041): PROBLEM SHEET 1, Solutions 1. a) No: 1.1(b) fails because d((0, 1), (1, 1)) = 0
- METRIC SPACES (MATH0041): PROBLEM SHEET 2 Reminder: I will mark any work you hand in to me.
- METRIC SPACES (MATH0041): PROBLEM SHEET 6, Solutions 1. i) X = C (usual metric); an = ein. Bounded as |an| 1. Not Cauchy or conver*
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- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 1: SOLUTIONS
- MATH0103 University of Bath
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 1
- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 2: SOLUTIONS
- FOUNDATION MATHEMATICS I (MATH0103): PROBLEM SHEET 2 Please hand in solutions to the following questions on Monday 16th October. The*
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 7
- NUMBERS (MA10001): PROBLEM SHEET 7 Hand in your solutions to questions 1, 2, and 4 to your tutors by 09:00 on Tuesday, 2nd
- MATHEMATICS 2 (MA10193) ASSESSED COURSEWORK
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 6
- INTRODUCTION TO TOPOLOGY (MA30055): PROBLEM SHEET 2 If you put solutions to this sheet in the folder on my door (1W3:35) or hand them to
- Abelian surfaces with odd bilevel structure G.K. Sankaran
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 1, SOLUTIONS
- NUMBERS (MA10001): PROBLEM SHEET 1 Hand in your solutions to questions 1 and 2 to your tutors by 09:00 on Tuesday, 14th
- ALGEBRAIC CURVES (MA40188): PROBLEM SHEET 1 I will look at any solutions you hand in, and return them to you in due course.
- NUMBERS (MA10001): INDUCTION FOR ELEPHANTS Induction, in the form we have seen it, is the rule that says that if P(n) is a statement
- NUMBERS (MA10001): REVISION SHEET This is a general revision sheet for the entire course. You use it as you see fit, but
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- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 5, SOLUTIONS
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 6
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 3, SOLUTIONS
- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 1
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 3
- METRIC SPACES (MATH0041): REVISION SHEET 1 1. Let (X, d) be a metric space and W X. Define the closure W~ of W in X.
- METRIC SPACES (MATH0041): PROBLEM SHEET 3 1. Show that if (an) is a sequence in a metric space with the property that eve*
- METRIC SPACES (MATH0041): PROBLEM SHEET 4, Solutions 1. If x 2 Y Othen there exists ffl > 0 such that Bffl(x) Y O, since Y Ois ope*
- FOUNDATION MATHEMATICS I (MATH0103): SOLUTIONS 6 Here are very brief solutions to Problem Sheet 6, without explanation.
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 4
- METRIC SPACES (MATH0041): PROBLEM SHEET 6 1. In each of the following cases, say whether the sequence (an) in the metric *
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 8, SOLUTIONS
- MATHEMATICS 2 (MA10193) EXAMPLES SHEET 3: SOLUTIONS
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 8
- FOUNDATION MATHEMATICS I (MATH0103): PROBLEM SHEET 6 Please hand in solutions to the following questions on Monday 13th November.
- PROGRAMMING AND DISCRETE MATHEMATICS 1 (XX10190) SEMESTER 2 MATHEMATICS: PROBLEM SHEET 7, SOLUTIONS
- FURTHER MATHEMATICAL TECHNIQUES (MA10193) EXAMPLES SHEET 2
- METRIC SPACES (MATH0041): PROBLEM SHEET 2, Solutions 1. a) Unbounded, e.g. because if M 2 R then d(iM, 3iM) = 2M > M.
- Moduli spaces of irreducible symplectic manifolds V. Gritsenko, K. Hulek and G.K. Sankaran