Completing a sub three hours marathon

Before reading this article about how you can prepare yourself for completing a sub three hours marathon, you may ask “why three hours and where does that point come from?”. Well, there are a couple of critical point for marathoners that they are trying to reach those points and they are 4:30,4:00,3:30 and 3:00 hours. Among those times, completing a sub three hours Marathon is specially important for marathoners because it would qualify them for Boston marathon which is dream of every marathoner. Actually to be very exact at this point, being qualified for Boston marathon depend on your age and gender, and for young men runners (under age 30) qualifying time for Boston marathon is 3:05 hours.

Sub Three Hour Marathon

There are different training schedules for marathon, but most of them consist of about 18 weeks of training and in this period you would run over  1100km. After completing each marathon, you need at least two weeks of rest before start training for your next marathon in order to improve your previous record. In case you want to start training for your next marathon immediately after your previous training, you may neglect the first five weeks of your schedule which doesn’t include SOS workouts and jump into the sixth week, but in any case in order to complete the rest of your schedule, you again need to train at least 13 weeks/+1000km in order to get your goal.

Now back to our initial question “how long would it take to complete a sub three hours marathon and be qualified for Boston marathon”, the math is very simple now. Usually to have a sub 3:30 marathon, you need at least two training sets while any attempt to complete your first marathon before 3:30 hours is pretty aggressive and chances of getting injured is so high, where in that case you would not even able to complete the marathon.

After completing a sub 3:30 marathon, by each set of training, you would able to improve your previous record by usually 3% ,let’s say 7 minutes (theoretically you can improve up to 5%, but again it’s not recommended and continuing that way you would high likely get injured in a close future) Therefore in order to improve your record from 3:30 hours to 3:00 hours you need 4 sets of marathon training and therefore you need at least six sets of training in order to be able to complete a sub three hours marathon from the point that you started. As we discussed in past each training set requires at least 1000 km of running so you need to run at least for 6000 km in order to complete a sub three hours marathon and being qualified for Boston marathon which is dream of every marathoners.

Operator Theory and It’s Applications

This course had a significant influence on my point of view on lot’s of different problems, from study of different ODE/PDE’s to even various kinds of “Optimization” problems, because technically all of those concepts (i.e. ODE/PDE’s or Optimization problems) are certain operators from one space to another. Below is details of what we covered in that course:

During this course we first had a review of Hilbert and Banach Spaces, then we fully studied different kinds of operators such as “Linear”, “Bounded”, “Compact”, “Hermitian”, “Self-Adjoint” and “Unitary” Operators. In the second part of the course we reviewed several versions of “Spectral Theorem” with proofs for it.

In the last part of the course we first studied several kinds of unbounded operators such as “Closed and Closeable, Symmetric and Self-Adjoint” unbounded operators and after that we learned Spectral and Bloch Theory for unbounded operators and the spectrum of periodic Schrodinger operators.

Functional Analysis

I made a strong foundation for my mathematical analysis through this course together with “Real Analysis and Measure Theory”. In the first part of the course we learned “Banach Spaces” , “Strong, Weak and Weak* Topologies”.

After that, we went through three important theorems which were “Hahn-Banach, Open Mapping and Closed Graph” Theorems. Hilbert spaces was the next topic we covered and at the end we covered two important theorems “Spectral Theory of Bounded Operators” and “Theory of Distributions”.

Complex Analysis

The importance of the course “Complex Analysis” for me was due to the fact that later on, I was able to apply it’s concepts in order to develop my theorem in “Fluid Dynamics” where there, I explained “The Behavior of Newtonian Fluids in Multiply Connected Domains”.

In this course we first reviewed “Continuous and Holomorphic Functions” on the complex plane and integration along the curves. In the second part we reviewed “Cauchy’s Theorem and it’s applications” especially on evaluation of some integrals. In the third part of the course we reviewed “Meromorphic Functions and the Logarithm” included “Homotopies and Simply Connected Domains”, “The Complex Logarithm” and “Fourier Series and Harmonic Functions”.

Finally in the last part of the course, we learned conformal mappings included “The Schwarz Lemma”, “The Riemann Mapping Theorem” and “Conformal Mappings onto Polygons”.

Real Analysis (Measure Theory & Integration)

I built a strong foundation for my mathematical analysis through this course together with the functional analysis course. At first we defined “Sigma Algebra and Measures”, then we defined “Integration” based on those definitions. In the next part we defined “Convergence of Functions”. After that we learned “Radon-Nikodym Theorem” and “Introduction to Lp Spaces”.

Linear Optimization

During the course “Linear Optimization” I got familiar with different methods of optimizing systems of linear inequalities with multiple variables. In particular, I got familiar with “Fundamental Theorem of Linear Programming”, “Weak Duality Theorem”, “Strong Duality Theorem”, “Complimentary Slackness Theorem”, “Economic Interpretation of Dual Variables” and “Karush-Kuhn-Tucker Conditions”.

Background in Science and Engineering

I believe my multiple background in science and engineering can be extremely useful for any team project and I would able to use my mathematical background to look at the project from a general point of view, find and create unique and specific solutions for it using my background in engineering and bring the project to the next level.

During my undergrad studies, I had the experience of looking at the techniques we learned in our engineering courses from an abstract point of view and even sometimes find a mathematical proof for them. Through practicing that method and by getting experienced in it, finally in my master thesis in mathematics, I was able to develop a mathematical theorem which was explaining the behavior of Newtonian’s flow in certain situation.

I believe that result, can totally explain my ability in looking at any project from a abstract point of view, generalize the problem and finally predict the solution for any problem in similar situations.

Complex Fluid (Math 559)

In this course we had an overview of Non-Newtonian Fluid Dynamics, and discussed two approaches for building constitutive models for complex fluids: continuum modeling and kinetic-microstructural modeling. We also learned about “multiphase complex fluids” and “numerical models and algorithms for computing complex fluid flows”. Through this course, I got a deep understanding of the fact that how we can apply different mathematical models for certain types of physical problems.

 

Master Thesis

Important Result:

Deriving a theorem in Fluid Dynamics which explains how boundary conditions would affect behavior of Newtonian fluids and obtaining numerical results using accurate numerical schemes.

Numerical Schemes Used in Thesis:

Spectral Methods, Compact finite differences (The most accurate scheme applicable to the problem)

Advanced Mathematical Techniques Used for Modeling the Problem:

Dynamical Systems, Linear Algebra, Complex and Real Analysis, Inversion Theory and Conformal Mapping, Topology.

Math Thesis Link

My Tutoring Style

The Organized, Patient Tutor: What I’ve heard multiple times from my students is “you are so organized and patient” and I believe those are the most important and necessary factors for any teacher. During my tutoring sessions, I listen carefully to my students to understand the parts that they are struggling with and after that we carefully go through those concepts and I’ll teach them their weaknesses until we make sure that they are no longer strange with those concepts.

Teaching Through Examples: I usually ask my students which way they prefer to study and most of my students prefer to study through problems of their assignments, specially online webwork assignments. So what we’ll do is we would go over their webwork assignments to see which problems they haven’t solved properly or even the problems that they have tried to solve it a couple of times and see which part they are struggling in it. After finding their weaknesses in those examples, we would solve a couple of similar problems either from their webwork problems or from the suggested problems of their textbook or old UBC exams to make sure they are pretty comfortable with the concepts that they were struggling with.

Conceptual Teaching: Some of my students prefer to learn through their textbook. This particularly happen for the conceptual courses where they are struggling with learning concepts of the course with themselves. Linear algebra and more advanced math courses and physics course are among them. In that case, we start reviewing the sections of the course where my students need helps in it and after teaching them the concepts, we solve a couple of examples from their textbooks, webwork problems, old UBC exams or other sources.

Crash Course Tutoring: Usually close to midterms or finals, some students ask me to review the entire course in a few sessions. What I’ll do for those students is I would prepare a summary of the important points of the course and we quickly go over all the materials of the course and at the end, in the areas that they feel they need more help in it, we would solve a couple of more examples to make sure they are totally ready for their exam.

Solving Old UBC Exams: Finally when it’s pretty close to the exam date, my students ask me to have a session to solve old UBC exams and in that case we solve some sample examples from old UBC mid/final exams.

My UBC Tutoring Experience

Tutoring of the following first year UBC Math courses:

  • Math 001 Pre-Calculus
  • Math 100 Differential Calculus
  • Math 101 Integral Calculus
  • Math 102 Differential Calculus
  • Math 103 Integral Calculus
  • Math 104 Differential Calculus
  • Math 105 Integral Calculus
  • Math 110 Differential Calculus
  • Math 121 Integral Calculus
  • Math 152 Linear Systems
  • Math 180 Differential Calculus
  • Math 184 Differential Calculus

Tutoring of the following first year UBC Physics courses:

  • Physics 101 Energy and Waves
  • Physics 118 Electricity, Light and Radiation
  • Physics 158 Introductory Physics for Engineers II
  • Physics 170 Mechanics I

Tutoring of the following second year UBC Math courses:

  • Math 215 Elementary Differential Equations
  • Math 220 Mathematical Proof
  • Math 221 Matrix Algebra
  • Math 255 Ordinary Differential Equations
  • Math 256 Differential Equation
  • Math 257 Partial Differential Equation
  • FRST 231 Introduction to Biometrics and Business Statistics

Tutoring of the following third year UBC Math courses:

  • Math 300 Complex Analysis
  • Math 312 Introduction to Number Theory
  • Math 316 Elementary Differential Equation II
  • Math 340 Introduction to Linear Programming

My Teaching Experiences at UBC

  • Teaching Assistant of Math 358 Engineering Analysis
  • Teaching Assistant of Math 317 Calculus IV
  • Teaching Assistant of Math 215 Elementary Differential Equation
  • Teaching Assistant of Math 102 Differential Calculus
  • Teaching Assistant of Pre-Calculus Math (Supervisor of Labs)
  • Instructor at Math Learning Center of UBC Mathematics Department