Problem Set 4 - The Finite-Dimensional Metric Space of Real Vectors

MOVIES - GREAT CONTRIBUTORS - PAUL ERDÖS

N is a Number: A Portrait of Paul Erdös




http://topdocumentaryfilms.com/portrait-of-paul-erdos/

MOVIES - GREAT CONTRIBUTORS: PAUL HALMOS

http://www.imdb.com/title/tt1417077/?ref_=fn_al_tt_1

EXAM 1 - PARTS 1 AND 2

MOVIES - GREAT CONTRIBUTORS TO MATHEMATICAL ECONOMICS - JOHN NASH

John Forbes Nash Junior renamed mathematician which surname is sinonyms of economic equilibria.
Nash Equilibria is a commom reference index of economic textbooks, mainly those on game theory or microeconomic theory. His life were interpreted by Russell Crowe.


http://www.imdb.com/title/tt0268978/?ref_=nv_sr_1

MOVIES - GREAT CONTRIBUTORS TO MATHEMATICAL ECONOMICS - DANIEL ELLSBERG

           In decision theory some paradoxes sourced from von Neumann-Morgenstern utilities, amongst them Ellsberg Paradox  were renamed during the sixties mainly because the properties of vN-M utility function. Daniel Ellsberg, in his short academic life, proposed a paradox to vN-M utility function and his controversial bureaucratic pentagon life was registered in movie.

http://www.imdb.com/title/tt1319726/?ref_=fn_al_tt_1

Problem Set 3 - Space of Real Numbers (Applied Mathematical Methods to Economics - Summer Course)

Exercises from Corbae, Stinchcombe, and Zeman (2009) – odd ones

Exercise 3.3.17 (Cauchy Sequences)

Exercise 3.3.31 (The Real Numbers: Definition and Basic Properties)

Exercise 3.4.7  (The Completeness of the Real Numbers)

Exercise 3.4.13 (The Completeness of the Real Numbers)

Exercise 3.5.3 (Geometric Sums)

Exercise 3.7.17 (Monotone Sequences)

Exercise 3.8.1 (Products of Sequences and e^x)

Exercise 3.9.3 (Lim inf and Lim sup)

Exercise 3.9.5 (Lim inf and Lim sup)

Exercise 3.9.11 (Discount Factors Close to One)

SOLUTION - PROBLEM SET 2 – PART 2 – SET THEORY (updated)

Exercise 2.2.5 (Notation and Other Basics)

Exercise 2.2.7 (Notation and Other Basics)

Exercise 2.2.13 (Products, Relations, Correspondences, and Functions)

Exercise 2.5.3 (Optimal Choice for Finite Sets)

Exercise 2.5.7 (Optimal Choice for Finite Sets)

Exercise 2.6.3 (Direct and Inverse Images, Compositions)

Exercise 2.6.5 (Direct and Inverse Images, Compositions)

Exercise 2.6.11 (Direct and Inverse Images, Compositions)

Exercise 2.6.19 (Direct and Inverse Images, Compositions)

Exercise 2.6.27 (Direct and Inverse Images, Compositions)

Exercise 2.7.9 (Weak and Partial Orders, Lattices)

Exercise 2.7.15 (Weak and Partial Orders, Lattices)

Exercise 2.8.3 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.11 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.13 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.15 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.19 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.8.21 (Monotonic Changes in Optima: Supermodularity and Lattices)

Exercise 2.9.3 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.15 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.19 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.23 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.27 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.9.29 (Tarski’s Lattice Fixed-Point Theorem and Stable Matchings)

Exercise 2.10.3 (Finite and Infinte Sets)

Exercise 2.10.11 (Finite and Infinte Sets)

Exercise 2.10.13 (Finite and Infinte Sets)

Exercise 2.10.17 (Finite and Infinte Sets)

Exercise 2.12.7 (Revealed Preference and Rationalizability)

Exercise 2.13.2 (Superstructures)

Exercise 2.15.1 (End-Chapter Problems)

Exercise 2.15.3 (End-Chapter Problems)

SOLUTION - PROBLEM SET 1 - PART 1 - LOGIC (updated)

1.1) and 1.2)

1.3) and 1.4)

1.5) and 1.6)

1.7)

1.8)

1.9)

1.10)

1.11)

1.12)

1.13)

1.14)

1.15)

1.16)

1.17)

1.18)

1.19)

1.20)

1.21) and 1.22)

1.23)

1.24)

1.25)

1.26)

1.27) and 1.28a)

1.28b)

2)

3)

4) and 5)

6)

7) Exercises from CSZ
1.3.3) 

1.3.5)

1.3.7)