Mathematics Ultralearning: The Outline

I will use this blog post as my "attack plan" of learning mathematics from the beginning, starting with proofs and discrete mathematics and ending with dynamical models in biology. This post is subject to change at any time. 

Goal: Re-teach myself mathematics in areas appropriate for bioinformatics.

Timeline

Dynamical models in biology requires prerequisites of Math 250 (Linear Algebra) and Calc IV (Elementary Differential Equations). Thus, the following classes are part of the expected coursework for this entire project, should I learn every prerequisite needed for each class:

• Precalculus* 
• Linear Algebra*
• Calculus I*
• Calculus II*
• Multivariable Calculus* 
• Elementary Differential Equations*
• Real analysis (optional) 
• Dynamical Models in Biology*

In addition, I am adding the following subjects to better round out my knowledge in mathematics:

• Introduction to Mathematical Reasoning (proofs)
• Logic (optional) 
• Discrete and Probabilistic Models in Biology

Each class/subject takes one semester's worth of time, a total of 5 years worth of learning at most. As it stands, most ultralearning projects choose to shorten that timeline. Young's ultralearning project itself, the MIT Challenge, condensed 4 years worth of MIT's computer science courses into one year.

I find myself reaching for a less ambitious roadmap. After all, I will still be working, and moreover, *I have taken almost all of these courses before. As such, the learning curve is flattened a bit, with less time needed on introductory courses and more time spent on relearning important concepts and maintaining accuracy. For example, I don't expect myself to spend a lot of time on precalculus as a subject, since I am already adept at it. 

Consequently, I will not be digesting 5 years' worth of information. I approximate this ultralearning timeline to take one year, learning 2.5 years' worth of information within that time span. I am giving myself permission to extend or decrease up to half a year.

Parts of Young's project intersect with mine, with Calculus, Linear Algebra, and Logic being part of the MIT OCW. I will use his resources where available but otherwise supplement these courses with textbooks that I obtain myself. 

Textbooks/Resources

• Khan Academy
• Linear Algebra (Friedberg, Insel, and Spence) 
• Calculus (Stewart) 
• Dynamical Models in Biology (Farkas)
• https://www.math.rutgers.edu/academics/undergraduate/201-course-materials/270-338/1255-course-notes
• An Introduction to Mathematical Reasoning (Eccles)
• Book of Proof (Hammack)

 

The Backstory of my Personal Curriculum and Ultralearning

The concept of ultralearning is, essentially, deep self-education to learn hard things in less time. Scott H. Young has written in the past about using this approach towards MIT's computer science courses, learning multiple languages, and learning cognitive science. It is intentional, active focus on subjects that are just at the edge of one's abilities, tempering the balance between too easy and too difficult. It is deep work.

I've read Young's Ultralearning time and time again, wondering what I could apply its principles to in my life. Finally did I land on a topic that serves both personal and professional interest: mathematics. Mathematics is a peculiar subject to ultralearn considering my background -- I am (was?) historically inept at math. I often near failed or outright failed my tests in high school. I had predetermined myself to just be "bad at math" and call it a day, certain I would not use this information any more in my future.

When I had entered university, I had learned quite the opposite. I found myself with a degree in physics. Math pervaded everything. How I ended up pursuing a physics degree is anyone's guess; perhaps it was a challenge to myself that I could persevere and learn a subject I originally thought myself to always be incompetent in. I thrived as I expanded my horizons of mathematics, learning more each passing day that I was capable of learning challenging concepts. I pushed the boundaries of my thinking. I passed differential equations, mechanics, and complex analysis and variables.

I graduated, and I tucked away the degree into a neat little corner of both my house and mind. What were my pathways now? I didn't want to go into academia, and I didn't have the money to get a master's degree. I went into nursing instead for its stability, at a loss for what to do, scrambling for a source of income. 

Nursing stayed as my "passion" until I was released from its grip by means of recent burnout. I was tired. I had spent too long trying to convince myself that nursing was the only choice I had in life, resulting from the mixture of familial pressure and societal obligation. I fondly looked back at my undergrad days. I wondered, and wondered often, if I could return to those times. 

Presently, I still work as a nurse for the financial support, nonetheless I have a plan in place: to self-teach mathematics and biology and pursue a master's in biostatistics. I have nursing to supplement the funds. It is never too late to live as my authentic self, one who enjoys mulling over number sets and data, one who enjoys the logic and rhythm of solving a math problem. I have lost a lot of my math skills and knowledge over time. Thus, ultralearning makes the most sense here -- this project's purpose is to polish and retrain my skills before diving in. It is, almost, a project of self-discovery.

So starts my journey.