Fall 2018

MAT1000HF / MAT457H1F · Real Analysis I Information Syllabus
Lectures
Mon
Wed
11:00AM 
10:00AM 
- 12:00PM
- 12:00PM
BA 6183
BA 6183
Office Hours
Mon
Wed
12:00PM 
12:00PM 
- 1:00PM
- 1:00PM
PG 201B
PG 201B
TA Office Hours
TBA
 

Teaching assistant
Malors Emilio Espinosa Lara Web page email
Textbook
Gerald B. Folland
Real Analysis: Modern Techniques and Their Applications
Second edition [first edition is acceptable]

Course schedule and additional material available on Quercus

Past courses

Fall 2017: MAT1000HF / MAT457H1F · Real Analysis I Information Syllabus
Lectures
Mon
Wed
11:00AM 
10:00AM 
- 12:00PM
- 12:00PM
BA 6183
BA 6183
Office Hours
Mon
Wed
12:00PM 
12:00PM 
- 1:00PM
- 1:00PM
PG 201B (← please note change!)
PG 201B
TA Office Hours
Fri
9:00AM 
- 11:00PM
BA 6180

Teaching assistant
Malors Emilio Espinosa Lara Web page email
Textbook
Gerald B. Folland
Real Analysis: Modern Techniques and Their Applications
Second edition [first edition is acceptable]

Course schedule and additional material

Sept 11
Course introduction, algebras, σ-algebras
Folland Chapter 1.1–2
Sept 13
Monotone class theorem, product spaces
Folland Chapter 1.2, Lieb-Loss Theorem 1.3
Note about the Monotone Class Theorem
Sept 18
Borel σ-algebra, Definition and basic properties of measures
Folland Chapter 1.3
Sept 20
Null sets and completion, outer measures, Carathéodory's Theorem, extension
Folland Chapter 1.3–4
Sept 25
Premeasures on an algebra and extension
Folland Chapter 1.4
Sept 27
Construction of the Lebesgue-Stieltjes measure; properties
Folland Chapter 1.5
Oct 2
Regularity of Lebesgue measure, examples
Folland Chapter 1.5
Some notes about Cantor Sets
Oct 4
Measurable functions, characteristic functions, simple functions and approximation
Folland Chapter 2.1
Oct 11
The rôle of null sets, Integration of simple functions and non-negative functions. Monotone Convergence Theorem and Fatou's Lemma.
Folland Chapter 2.2
Oct 16
Integral of complex-valued functions, L¹ as a vector space, Dominated Convergence Theorem
Folland Chapter 2.3
Oct 18
Proof of the Dominated Convergence Theorem, Normed vector spaces, completeness criterion, Banach spaces.
Folland Chapter 2.3, 5.1
Oct 23
Lp spaces, Hölder inequality and Minkowski inequality.
Folland Chapter 2.3, 6.1
Oct 25
L space, ℓp spaces, interpolation inequalities. Bounded linear operator and functionals on Banach spaces
Folland Chapter 6.1, 5.1
Oct 30
Midterm review session
Nov 1
Midterm exam (room EX200)
Nov 13
Dual of Lp
Folland Chap. 6.2
Nov 15
Lebesgue vs Riemann Integral, modes of convergence, Product measures
Folland Chap 2.3–5
Nov 20
Signed measures, Hahn and Jordan Decomposition, absolute continuity
Folland Chap 3.1–2
Nov 22
The Radon-Nikodym-Lebesgue Theorem
Folland Chap 3.2-3.3
Nov 27
Complex measures, the dual of Lp
Folland Chap 3.3 6.2
Nov 29
Differentiation on Euclidian space
Folland Chap 3.4

Homework assignments

Each homework assignment will become available for download at least one week prior to the corresponding due date

Homework 1
 (due on Sept 20 10:20 AM)
  Download Updated on Sept 18
Homework 2
 (due on Sept 27 10:20 AM)
Homework 3
 (due on Oct 04 10:20 AM)
Homework 4
 (due on Oct 11 10:20 AM)
Homework 5
 (due on Oct 18 10:20 AM)
Homework 6
 (due on Oct 25 10:20 AM)
Homework 7
 (due on Oct 30 11:20 AM)
  Download Updated Oct 27
Homework 8
 (due on Nov 15 10:20 AM)
Homework 9
 (due on Nov 22 10:20 AM)
Homework 10
 (due on Nov 29 10:20 AM)
Homework 11
 (due on Dec 06 10:20 AM)
Homework n+1
 (do not hand in)

Midterm practice problems

Midterm practice problems 1
Midterm practice problems 2
  Download Corrected on Oct 26
Midterm practice problems 3
  Download Updated on Oct 30
Solution to problem 3.1
Fall 2016: MAT1844HF · Nonlinear dynamical systems: stochastic properties Information Syllabus
Lectures
Mon 11:00AM - 1:00PM
Wed 11:00AM - 12:00PM
BA 6180
BA 6180
Office Hours
Mon 2:00PM - 3:00PM
Wed 12:00PM - 1:00PM
PG 201A
PG 201A

Fall 2016: MAT332HF · Introduction to nonlinear dynamics and chaos Schedule Syllabus Course evaluations
Lectures
Tue 3:00PM - 5:00PM
Thu 1:00PM - 2:00PM
IB 377
IB 377
Tut 0101
Mon 2:00PM - 3:00PM
DV 1161
Office Hours
Tue 2:00PM - 3:00PM
Thu 2:00PM - 3:00PM
DH 3040
DH 3040

Information (including course evaluations) for courses that I gave as a Post-Doctoral fellow at UTM can be found here.