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please take the three handouts, and start filling out the exciting survey. MathTools for Neuroscience. Greg. Ilana. Today:. Introduction Equations are your friends <break> Remember Calculus?. The two questions:. What am I going to learn?. Math. a foreign language:. Why should I care?.
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What am I going to learn?
Math
a foreign language:
Why should I care?
Because you will be tested on it.
To calculate stuff
To prove stuff
To understand
to express, to describe, to communicate
just like a language
transcendence
her, him,
somestuff
3, π, ∞
nouns:
pronouns:
x, y,
verbs:
run, conjure
+, ∫ dx
clauses:
the gray cat
3x2
sentences:
God is dead.
E = mc2
…why can’t you all just speak English?
Mathis aspeciallanguage
Universal and Stable
Precise, Unambiguous Expression
Truth-Preserving Manipulation
Broad Introduction
Intuition & Comfort
Solid Statistics
Read Any Paper
Propose Novel Analyses
Website
mathtools.stanford.edu
It’s a statement.
‘is the numerical value’
‘is equivalent to’ ‘can be rewritten as’
Evaluation - ‘has the numerical value’
Equivalence - ‘can be rewritten’
Description
Evaluation - ‘has the numerical value’
Equivalence - ‘can be rewritten’
Description
‘is defined as’ ‘has the form’
Evaluation - ‘has the numerical value’
MATLAB
Arithmetic(get a calculator)
Equivalence - ‘can be rewritten’
Manipulation(get a geek)
Mathematica
Description - ‘has the form’
Science(get a clue)
Evaluation - ‘has the numerical value’
MATLAB
Arithmetic(get a calculator)
Equivalence - ‘can be rewritten’
Manipulation(get a geek)
Mathematica
Description - ‘has the form’
Science(get a clue)
Mappings from Input to Outputs
Evaluation - Arithmetic (a la MATLAB)
(e.g. 17 - 5 * 3 = 2 )
Equivalence - Manipulation (a la Mathematica)
(e.g. 2x + 3x = 5x )
Description -Science
Functions - relating input to output
(e.g. sinusoidal oscillation)
Metrics
Evaluation - Arithmetic (a la MATLAB)
(e.g. 17 - 5 * 3 = 2 )
Equivalence - Manipulation (a la Mathematica)
(e.g. 2x + 3x = 5x )
Description -Science
Functions - relating input to output
(e.g. sinusoidal oscillation)
Metrics
Evaluation - Arithmetic (a la MATLAB)
(e.g. 17 - 5 * 3 = 2 )
Equivalence - Manipulation (a la Mathematica)
(e.g. 2x + 3x = 5x )
Description -Science
Functions - relating input to output
(e.g. sinusoidal oscillation)
Metrics - formulaic ‘something-ness’
(e.g. variance and mean)
I. Consider the Context
Variables: x, y, z, t, v, u
other content based names
Parameters: , a, b, m
Indices: i, j, k, m, n
Special Numbers: e, i,
I. Consider the Context
II. Identify the Variables
III. Chunk It
IV. Consider the Form(s)
I. Consider the Context
II. Identify the Variables
III. Chunk It
IV. Consider the Form(s)
V. Imagine the Effect of Change
Fruit Salad!!!
Neuroscience Examples:
Notation:
Neuroscience Examples?
g(x) <-> f(x)
