This is an intensive 5-month timetable, but it also represents a life and career dedication that I'm fully ready to embrace. It demonstrates my commitment to ensuring I'm thoroughly prepared for success in this program.
I designed this schedule to prepare myself from April to August 2025 for the September 2025 Master Summer Refreshing Camp in Mathematics. The timetable maintains consistent daily time slots while allowing for comprehensive coverage over the entire 5-month period.
Daily Schedule
05:00 - 05:30: Morning Devotion
05:30 - 08:00: Analysis Study
April: Real Analysis Foundations
- Canuto & Tabacco's "Mathematical Analysis I"
- Week 1: Ch. 1 (Sets, mathematical logic, sets of numbers)
- Week 2: Ch. 2 (Functions, definitions, elementary functions)
- Week 3: Ch. 3-4 (Limits and continuity I & II)
- Week 4: Ch. 5 (Local comparison of functions, sequences, series)
- Exercises: From Canuto & Tabacco (end of each chapter)
May: Advanced Real Analysis
- Canuto & Tabacco
- Week 1: Ch. 6 (Differential calculus, derivatives, extrema)
- Week 2: Ch. 7 (Taylor expansions and applications)
- Week 3: Ch. 9 (Integral calculus I, primitive functions, Riemann integral)
- Week 4: Ch. 10 (Integral calculus II, improper integrals)
- Exercises: Abbott's "Understanding Analysis" (Ch. 1-2: 1.3.2, 1.3.6, 2.2.4, 2.3.2, 2.4.6, 2.5.7)
June: Complex Analysis Fundamentals
- Bak & Newman's "Complex Analysis"
- Week 1: Ch. 1 (The Complex Numbers: field properties, complex plane)
- Week 2: Ch. 2 (Functions of Complex Variable z: analytic polynomials, power series)
- Week 3: Ch. 3 (Analytic Functions: Cauchy-Riemann equations)
- Week 4: Ch. 4 (Line Integrals and Entire Functions)
- Exercises: Bak & Newman's "Complex Analysis" (end of each chapter)
July: Advanced Complex Analysis
- Bak & Newman's "Complex Analysis"
- Week 1: Ch. 5 (Properties of Entire Functions: Cauchy integral formula)
- Week 2: Ch. 6 (Properties of Analytic Functions)
- Week 3: Ch. 9-10 (Isolated Singularities, Residue Theorem)
- Week 4: Ch. 11 (Applications of the Residue Theorem)
- Exercises: Bak & Newman's "Complex Analysis" (end of each chapter)
August: Ordinary Differential Equations
- Canuto & Tabacco - Ch. 11 (Ordinary differential equations)
- Week 1: First-order differential equations (11.2.1-11.2.3)
- Week 2: Linear equations and initial value problems (11.2.2, 11.3)
- Week 3: Second-order equations with constant coefficients (11.4)
- Week 4: Review of all Analysis topics
- Exercises: Problems from Ch. 11
Video Resources
- Steve Brunton's YouTube series:
- "Differential Equations and Dynamical Systems" (https://youtu.be/9fQkLQZe3u8)
- "Complex Analysis" (https://youtu.be/_mv0q7-WF4E)
08:00 - 08:30: Breakfast Break
08:30 - 10:30: Linear Algebra & Topology
April: Vector Spaces and Linear Maps
- Hoffman & Kunze's "Linear Algebra"
- Week 1: Ch. 2 (Vector Spaces)
- Week 2: Ch. 3 (Linear Transformations and Matrices)
- Week 3: Ch. 4 (Polynomials)
- Week 4: Ch. 5 (Determinants)
- Exercises: Wadsley's Linear Algebra exercises (1.2, 1.4, 1.7, 1.9, 2.1, 2.3)
May: Advanced Linear Algebra
- Hoffman & Kunze's "Linear Algebra"
- Week 1: Ch. 8 (Inner Product Spaces)
- Week 2: Ch. 8 (Linear Functionals and Adjoints, Section 8.3)
- Week 3: Ch. 10 (Bilinear Forms)
- Week 4: Ch. 10 (Bilinear Forms continued)
- Exercises: Wadsley's Linear Algebra exercises (2.6, 2.8, 3.2, 3.5, 3.7, 3.9, 4.1, 4.4)
June: Basic Topology Concepts
- Munkres' "Topology: A First Course"
- Week 1: Ch. 1 (Set Theory and Logic)
- Week 2: Ch. 2 (Topological Spaces and Continuous Functions, Sections 2.1-2.7)
- Week 3: Ch. 2 (The Product Topology, Sections 2.8-)
- Week 4: Ch. 2 (The Product Topology continued)
- Exercises: Rasmussen's Topology exercises (1.1, 1.3, 1.6, 1.8, 2.2, 2.4)
July: Advanced Topology
- Munkres' "Topology: A First Course"
- Week 1: Ch. 3 (Connectedness, Sections 3.1-3.2)
- Week 2: Ch. 3 (Path connectedness, Sections 3.3)
- Week 3: Ch. 3 (Compactness, Sections 3.5)
- Week 4: Ch. 4 (Separation axioms, Sections 4.2)
- Exercises: Rasmussen's Topology exercises (2.7, 3.1, 3.3, 3.6, 4.2, 4.5, 4.8)
August: Review of Linear Algebra and Topology
- Week 1: Review of Vector Spaces and Linear Maps
- Week 2: Review of Advanced Linear Algebra
- Week 3: Review of Basic Topology Concepts
- Week 4: Review of Advanced Topology
- Exercises: Comprehensive review problems
Video Resources
- Professor Macauley's Linear Algebra playlist (https://www.youtube.com/playlist?list=PLwV-9DG53NDwKJIwF5sANj6Za7qZYywAq)
- DanielChanMaths' Point-set Topology playlist (https://youtu.be/b3EQQfi7xIc)
10:30 - 11:00: Short Break
11:00 - 13:00: Measure Theory & Probability
April: Measure Theory Fundamentals
- E. Çınlar's "Probability and Stochastics" (Part I, Chapters 1-2)
- Week 1: Ch. 1 (Measurable Spaces)
- Week 2: Ch. 2 (Measurable Functions)
- Week 3: Ch. 3 (Measures)
- Week 4: Ch. 4 (Integration)
- Exercises from E. Çınlar's "Probability and Stochastics" (end of each chapter)
May: Lebesgue Integration
- E. Çınlar's "Probability and Stochastics" (Part I, Chapters 4-5)
- Week 1: Ch. 4 (Integration)
- Week 2: Ch. 4 cont. (Measurable functions and their integration)
- Week 3: Ch. 5 (Transforms and Indefinite Integrals)
- Week 4: Ch. 6 (Kernels and Product Spaces)
- Exercises from E. Çınlar's "Probability and Stochastics" (end of each chapter)
June: Product Measures and Fubini Theorem
- E. Çınlar's "Probability and Stochastics" (Part I, Chapter 6)
- Week 1: Ch. 6 (Kernels and Product Spaces)
- Week 2: Product sigma-algebras
- Week 3: Ch. 6 cont. (Fubini's theorem)
- Week 4: Applications of Fubini-Tonelli theorems
- Exercises from E. Çınlar's "Probability and Stochastics" (end of each chapter)
July: Probability Theory Foundations
- E. Çınlar's "Probability and Stochastics" (Part II, Chapters 1-3)
- Week 1: Ch. 1 (Probability Spaces and Random Variables)
- Week 2: Ch. 2 (Expectations)
- Week 3: Ch. 3 (Lp-spaces and Uniform Integrability)
- Week 4: Ch. 5 (Independence)
- Exercises: Notre Dame's "Notes on Elementary Probability" selected problems
August: Advanced Probability Concepts
- E. Çınlar's "Probability and Stochastics" (Part IV, Chapters 1-3)
- Week 1: Ch. 1 (Conditional Expectations)
- Week 2: Ch. 2 (Conditional Probabilities and Distributions)
- Week 3: Ch. 3 (Conditional Independence)
- Week 4: Review of all Measure Theory and Probability topics
- Exercises from E. Çınlar's "Probability and Stochastics" (end of each chapter)
13:00 - 14:00: Lunch Break
14:00 - 15:30: Basketball
I love playing and practicing basketball as a physical activity for my mental refresh, and team building skills.
15:30 - 16:00: Rest
16:00 - 18:00: Advanced Topics & Applications
April: Advanced Calculus Applications
- Callahan's "Advanced Calculus: A Geometric View"
- Week 1: Ch. 3 (Approximations - Mean value theorems)
- Week 2: Ch. 4 (The Derivative - Differentiability)
- Week 3: Ch. 5 (Inverses - Solving equations)
- Week 4: Ch. 6 (Implicit Functions - A single equation)
- Exercises: Selected problems from Callahan
May: Vector Analysis
- Callahan's "Advanced Calculus" (later chapters)
- Week 1: Ch. 8 (Double Integrals)
- Week 2: Ch. 9 (Evaluating Double Integrals)
- Week 3: Ch. 10 (Surface Integrals)
- Week 4: Ch. 11 (Stokes' Theorem)
- Exercises: Selected problems from Callahan
June: Algebraic Structures
- Dummit & Foote's "Abstract Algebra" (selected chapters)
- Week 1: Group theory fundamentals
- Week 2: Subgroups and quotient groups
- Week 3: Ring theory basics
- Week 4: Ideals and quotient rings
- Exercises: Problems from Dummit & Foote and Goedecke's exercises
July: Field Theory and Applications
- Dummit & Foote's "Abstract Algebra" (field theory chapters)
- Week 1: Field extensions
- Week 2: Algebraic extensions
- Week 3: Splitting fields
- Week 4: Finite fields and applications
- Exercises: Problems from Dummit & Foote and Birkar's exercises
August: Integration of Mathematical Topics (unclear at the moment about the details yet)
- Focus on connections between different areas
- Week 1: Analysis and algebra connections
- Week 2: Topology and analysis connections
- Week 3: Measure theory and analysis connections
- Week 4: Comprehensive review across all topics
- Exercises: Integrative problems requiring multiple mathematical areas
Resources
- Needham's "Visual Complex Analysis" for geometric intuition
- MathDoctorBob's YouTube channel for Algebra (https://youtu.be/aENEYDFQnfA)
- Richard Borcherds' YouTube channel for advanced topics
18:00 - 18:30: Short Break
18:30 - 21:00: Problem-Solving Practice & Review
Monthly Problem Focus
April: Fundamental problems in real analysis and linear algebra
- Abbott's "Understanding Analysis" Ch. 1-2 exercises (1.2.3, 1.2.7, 1.3.2, 1.3.6, 1.4.1, 1.4.8)
- Wadsley's Linear Algebra exercises (vector spaces, linear maps)
May: More advanced problems in real analysis and linear algebra
- Abbott's "Understanding Analysis" Ch. 3-4 exercises (3.2.5, 3.3.4, 3.4.2, 4.2.4)
- Wadsley's Linear Algebra exercises (determinants, eigenvalues)
June: Problems in complex analysis and topology
- Bak & Newman end-of-chapter exercises from Ch. 3-6
- Rasmussen's Topology exercises (topological spaces, continuity)
July: Problems in measure theory and advanced topology
- Exercises from E. Çınlar's "Probability and Stochastics" (Part I, Ch. 1-4)
- Rasmussen's Topology exercises (connectedness, compactness)
August: Comprehensive and integrative problems (unclear at the moment about the details yet)
- Focus on questions that require multiple mathematical areas
- Past refresher camp exercises if available
21:00 - 23:00: Dinner, Family & Evening
Dinner, spend time with family, friends (both social media interactions and video gaming), and evening news.