Part A - Functions
This first part of Module 1 is called Part A. It is made of three brief videos, lasting in total 35 minutes. They offer an informal and elementary presentation, refreshing of the notion of a mathematical functions that you might have widely encountered in high school and, especially, during foundational courses (in math and physics) of your academic training. Ultimately, functions serve us as fundamental metaphors and are pivotal for the progression of quantitative Neurobiology, Biophysics, and Computational Neuroscience.
During our course, referring to and manipulating functions will be a powerful tool 1) to precisely identify the (bio)physical properties of neurons, synapses, and networks and 2) to predict or explain how they change in time and/or space. We do NOT do math for the sake of math! Should you initially feel differently, bear with me and trust my experience on brushing off your math background knowledge, aiming at further building up on it, and ultimately interested in a quantitative way of understanding neurobiology.
A recomendation
While watching these videos (and attending classes too), please do take notes - despite the videos or overheads availability. Also do use paper and pen, instead of a keyboard. Regaining your own confidence in writing and manipulating mathematical symbols is of utmost importance. Trust me: watching or listening passively this course will leave you no knowledge and you will forget the course content very soon. It would be a pity as you are investing your precious time! But be reassured: this (course) is neither special nor difficult, although it certainly departs from old-fashioned descriptive and qualitative treatment of biology. Neuroscience, and more in general Life Sciences, have now grown up into quantitative disciplines, where skills in math, physics, and computers are necessary and not optional.
Let's dive into it
Click on the image(s) below to watch the videos in a sequence.
Download if needed, the overheads from here.
Let's now move away from abstract definitions. Let me help you developing a intuitive understanding of the graph of (some) functions. You might call it algebra of functions' graphs. In the next video below, we will play with very simple manipulations to a mathematical function and understand how these are reflected visually on its graph. That's a convenient way to appreciate and understand functions.
Click on the image to watch the second video below.
If you feel brave, or perhaps intrigued by those sort of interactive manipulations, you can play a bit with this web site or with the interactive notebook below (hint: click on Open in Colab button). For both, you need curiosity and a web browser. For the latter, you might perhaps be tempted to look behind the scenes on how I built the code on what is Google Colab and how it works. Fear nothing! You can't break things!
Let's now go to the final video of this part. Click on the image to watch the third and last video below.
Now you should have a bit of familiarity with some notable functions. They are so simple to remember qualitatively and sketch on paper, when needed: straight lines, exponentials, and logarithms.
