Foundations of Mathematics
2017/4, MAW&MN
Assignment 5
(For Monday, 22 May)
Q1. (i)
Prove: An infinite subset of N is recursive if and only if it is the range of a strictly increasing
recursive functi
ESTIMATES AND ELLIPTIC EQUATIONS
JOHN URBAS
1. Why We Need Estimates
The aim of this lecture is to explain why we need various technical
estimates in PDE theory. The basic reason is that estimates of
ELLIPTIC DIFFERENTIAL EQUATIONS
OF DIVERGENCE FORM
QING HAN
Contents
1.
2.
3.
4.
Growth of Local Integrals
Schauder Theory
DeGiorgi Iterations
Mosers Iterations
2
6
14
22
In this note, we discuss the
Notes on the p-Laplace equation
Peter Lindqvist
Contents
1. Introduction
2
2. The Dirichlet problem and weak solutions
6
3. Regularity theory
16
3.1. The case p > n . . . . . . . . . . . . . . . . . .
Foundations of Mathematics
Assignment 2
Zhengyuan(Albert) Dong
u5343619
March 27, 2017
1. Prove
(x)(P Q) (x)P (x)Q.
Solution:
In this proof, c and d are fresh variables, and subdeductions are colored
Unit:
ACC101 Fundamentals of Accounting I
Weighting:
The assignment is worth 40% of the total unit weight.
Instructions:
1. Students are required to cover all stated requirements.
2. Your answer must
Foundation of Mathematics
Assignment 4
Zhengyuan(Albert) Dong
u5343619
May 10, 2017
1. Prove that the set of all countable ordinals is itself uncountable.
Solution:
Denote by a the set of all countabl
Foundations of Mathematics
2017/1, MAW&MN
Practice Test specimen solutions
Here are some specimen solutions to the Practice Test. I dont know why I am providing these because the
Practice Test is only
Foundations of Mathematics
2017/1, MAW&MN
Assignment 1
(For Friday, 10 March)
Q.1 These questions are about theories and entailment in a given language with a given set of rules. (Proposition 2.B.12 i
Foundations of Mathematics
2017/1, MAW&MN
Practice Test
(Not for handing in)
This is meant to give an idea of the format and general level of difficulty of the final test. It is not meant
to be an ind
Foundations of Mathematics
2017/4, MAW&MN
Assignment 4
Q1.
Q2.
(For Monday, 8 May)
Prove that the set of all countable ordinals is itself uncountable.
[1 mark]
Assume that and are countable ordinals.
Foundations of Mathematics
2017/1, MAW&MN
Assignment 3
Q.1
(For Tuesday, 25 April)
Prove that AC AC3 (see 6.F.3 in the notes).
Q.2 In the notes, Section 6.G.1 we prove that every vector space has a ba
Regularity of the Derivatives of Solutions
to Certain Degenerate Elliptic Equations
JOHN L. LEWIS
Introduction. In this paper we show for fixed p, 1 < p < 00, that if u is a
weak solution to V - (quIP
Foundation of Mathematics
Assignment 5
Zhengyuan(Albert) Dong
u5343619
May 25, 2017
1. (i) Prove: An infinite subset of N is recursive if and only if it is the range of a strictly
increasing recursive
Foundation of Mathematics
Assignment 3
Zhengyuan(Albert) Dong
u5343619
April 26, 2017
1. Prove that AC AC3 (see 6.F.3 in the notes).
Solution: We show first AC AC3 . Let A be a set of pairwise disjoin
Chin. Ann. Math.
27B(6), 2006, 637642
DOI: 10.1007/s11401-006-0142-3
Chinese Annals of
Mathematics, Series B
c The Editorial Office of CAM and
Springer-Verlag Berlin Heidelberg 2006
Schauder Estimates
Unit:
Weighting:
ACC102 Fundamentals of Accounting II
The assignment is worth 40% of the total unit weight
Instructions:
1.
Students are required to cover all stated requirements.
2.
3.
Your answer mu