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I am a Mathematics PhD student at the University of Washington, focusing on Algebraic Number Theory as it relates to Cryptology. I used to live in California, but I enjoy the cold weather so I think it is a lot nicer up here in Seattle. Being a PhD student, a majority of my time is spent doing mathematics, but during my free time I practice computer programming or mess around on an instrument. I used to play piano and violin quite a bit, but over the years I have played less, and it is just an occasional hobby now. Of course, despite my busy schedule I always make time to hang out with friends, whether through gaming or otherwise, just to keep myself sane whilst being immersed in academia.

Through tutoring, I wish to inspire those who have yet to see the wonders of mathematics in the hopes that they too might want to further the field themselves one day. As Edward Frenkel said in an interview on the subject of mathematics, “This is the coolest stuff in the world—that’s what it is … and yet everyone hates it. Isn’t it ironic?” Students are taught mathematics in a way that obscures its true beauty, and it is my hope that I can teach students in a way that encourages them, instead of deterring them.

Caleb’s Qualifications

Education & Certification

Undergraduate Degree: University of California-Irvine - Bachelors, Mathematics

Graduate Degree: University of Washington-Seattle Campus - Current Grad Student, Mathematics


Computer Programming, Novel Writing, and Gaming.

Q & A

What is your teaching philosophy?

A student who doesn't understand a problem hasn't been shown it in the correct light.

What might you do in a typical first session with a student?

Understand the student's foundation so as to be able to guide them through their problems.

How can you help a student become an independent learner?

During the session, you should have the student answer the questions themselves. Just giving them the answers does not help them learn.

How would you help a student stay motivated?

The results of the mathematics can often be their own motivation. If the student sees a problem as pointless or unnecessarily complicated, then you should show them where the problem is likely to help them later or where it can be applied.

If a student has difficulty learning a skill or concept, what would you do?

Often when a student has difficulty, it is because the way that the problem is presented is obscuring the fundamental portion of the solution that they're missing. Presenting a problem in multiple ways helps the student find one that works best for them.

How do you help students who are struggling with reading comprehension?

Mathematics is not a passive subject. You should have a piece of paper and a pencil out with you as you read to take notes, do problems, etc. This will greatly increase retention vs. reading how to do problems.

How do you build a student's confidence in a subject?

Practice is a student's best friend! It may not be the thing that a student wants to hear, but how can you get better and feel more confident in your abilities without practice?

How do you adapt your tutoring to the student's needs?

My tutoring style can assuredly vary from student to student. In the beginning, I try to figure out which ways I can present material that seem to "click" with the student, receiving both verbal and concrete (through their work) feedback on each method of tutoring.

What strategies have you found to be most successful when you start to work with a student?

This is a two person job. The student cannot expect through some magic that their problems will be solved just by showing up to a tutoring session. The students who do best in their classes are those who take what they've gained in the session and practice it to the point where the method of solving each problem is not a mystery, but is intuitive.

What types of materials do you typically use during a tutoring session?

For most sessions their book, a stack of paper, and a pencil or two is really all you need.

How would you help a student get excited/engaged with a subject that they are struggling in?

I frequently get excited about math, and I try to pass this excitement onto the student by showing them the aspect of the problems that motivate me or what aspects of the problem are useful for later and how that may be intriguing.

What techniques would you use to be sure that a student understands the material?

There are many ways to present each math problem, and by asking leading questions, the students can often answer their own questions with the right hint or prompt. When a student figures something out for themselves, rather than being told the information, it has a much higher retention rate.

How do you evaluate a student's needs?

Both verbally and through watching their work. Sometimes students know exactly what they need/do not understand. Other times, they are not sure, and we will run through a few problems to find troublesome points.