Analytics (for Everything) (⋆⋆)

Each of the sub-topics below will be applied to examples in the following list:

Systems biosciences (biochemical, molecular, cellular, tissue-level, organismal physiology, neuroscience, medicine, populations)
Cognitive psychological sciences
Computer (software) engineering
Computational Neuroscience
Economic sciences
All other physical engineering sciences.

There will be an emphasis on mathematical fluency/literacy; that is, a full comprehension to solve problems, and mathematical languages in the form of equations, numerical & symbolic formulations, and other graphical & diagrammatic representations.

Sub-topics

Induction
Trigonometry
Geometry
Cartesian maths
Functional mapping
Sequences & limits, series
Multivariate analytics
Complex numbers
Vectors, scalars, and matrices
Infinitesimal calculus
Differentiation, fist-order, higher-order, partial
Integration
Exponentials and logarithms
Transformations
Linear algebra
Non-linearity
Discrete mathematics
Group & set theory
Probability and statistics
Dynamics
Modelling
Theoretical & abstract mathematics
Graph theory
Fluid dynamics
Topology
Logic
Computation
Innovation in maths

A lot of scientists understand the language of mathematics and physics; and they understand the main concepts and structures studied within biology. But when we look at the underlying processes which support biophysical systems, we realise there is a lot more complexity than we had originally thought. Simple ideas, simple processes, laws, and simple building blocks, can give rise to ever-increasing combinatorial complexity. 'Complexity & Systems Science' is a rather new field of study, which is taking interdisciplinary science to its next level, and is really the only way to truly understand how things work, at every level of analysis.

Useful sources:

● https://www.ucl.ac.uk/complex (Centre for Mathematics and Physics in the Life Sciences and EXperimental Biology)

List of all equations

http://math.mit.edu/research/applied/index.php

https://bulletin.brown.edu/the-college/concentrations/apmb/

Applied math

https://mbi.osu.edu/programs/emphasis-programs/previous-programs/mathematical-neuroscience-2012-2013/

http://www.nature.com/neuro/journal/v4/n2/abs/nn0201_113.html

Brain calculus: neural integration and persistent activity

http://www-math.mit.edu/~djk/calculus_beginners/

https://brilliant.org/math/combinatorics/

Discrete Mathematics

https://en.wikipedia.org/wiki/List_of_equations

https://en.wikipedia.org/wiki/List_of_mathematical_functions

--- http://www.mathplanet.com/education/algebra-2/how-to-graph-functions-and-linear-equations

--- http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx

--- http://www.maths.ed.ac.uk/school-of-mathematics/studying-here/undergraduate-study/what-will-i-study

--- http://www.seemath.com/

--- http://animated-mathematics.net/

--- http://www.mathwarehouse.com/animated-gifs/

--- https://commons.wikimedia.org/wiki/Category:Mathematical_animations

--- http://www.science-animations.com/MathsAnimations.html

Some videos from external sources:

"On the Nature of Causality in Complex Systems, George F.R. Ellis" by Copernicus Center for Interdisciplinary Studies

http://youtube.com/watch?v=nEhTkF3eG8Q

"Complex Biological Systems: A Debate, pt. 1: Stephen Meyer Presents" by Stephen Meyer

http://youtube.com/watch?v=f36Xup_XN4M

"Open Science, Evolutionary Informatics, & the Tree of Life" by BRNINBRE

http://youtube.com/watch?v=DvzMnnX6xyI

"Information, Evolution, and intelligent Design - With Daniel Dennett" by The Royal Institution

http://youtube.com/watch?v=AZX6awZq5Z0

Creative Commons (free to use, share or modify, even commercially) Images, Animations and Videos

--- https://en.wikipedia.org/wiki/Unit_circle#/media/File:Circle-trig6.svg
--- http://texample.net/tikz/examples/observer-estimator/
--- https://commons.wikimedia.org/wiki/File:NonConvex.gif
--- https://commons.wikimedia.org/wiki/File:Euler-bqf-2x2.PNG
--- https://en.wikipedia.org/wiki/Portal:Mathematics/Selected_picture#/media/File:Villarceau_circles.gif
--- https://en.wikipedia.org/wiki/K-means_clustering#/media/File:K-means_convergence.gif
--- https://commons.wikimedia.org/wiki/File:NetworkTopologies.svg
--- https://commons.wikimedia.org/wiki/File:IQ_-_distribui%C3%A7%C3%A3o_sim%C3%A9trica.gif

--- "Algebra and Mathematics. Explained with easy to understand 3D animations." by Physics Videos by Eugene Khutoryansky (Jan 2014)
https://www.youtube.com/watch?v=MJYsXGbxueY
--- "Advanced Mathematics for Engineers Lecture No. 14" by Hochschule Ravensburg-Weingarten (Jan 2012)
https://www.youtube.com/watch?v=3rHBCglD1LQ