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please take the three handouts, and start filling out the exciting survey

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## please take the three handouts, and start filling out the exciting survey

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**please take the three handouts,and start filling out the**exciting survey**MathToolsforNeuroscience**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? Because you will be tested on it.**Why Is Important for a Neuroscientist to Learn Math?**To calculate stuff To prove stuff To understand to express, to describe, to communicate just like a language**cat, truth,**transcendence her, him, somestuff Mathis a language 3, π, ∞ nouns: pronouns: x, y, verbs: run, conjure +, ∫ dx clauses: the gray cat 3x2 sentences: God is dead. E = mc2**a foreign language?**…why can’t you all just speak English? But I’m an American… Mathis aspeciallanguage Universal and Stable Precise, Unambiguous Expression Truth-Preserving Manipulation**Why do we care?**Analysis Description**Why do we care?**Statistics Description**Why do we care?**Statistics Modeling**Who is the course for?**Survey Review**What are the Goals?**Broad Introduction Intuition & Comfort Solid Statistics Read Any Paper Propose Novel Analyses**What are the Goals?**I. The Basics II. Probability and Statistics III. Advanced Topics**But I’m Not A Systems Neuroscientist**Cognitive Neuroscience Molecular Genetics**Technical Stuff**Website**Technical Stuff**mathtools.stanford.edu**Technical Stuff**mathtools.stanford.edu Problem Sets**Technical Stuff**mathtools.stanford.edu Problem Sets Survey & Sign Up Sheet Lecture Notes Feedback**Equations are Your Friends**How to Speak Math Your Pet Equation**Why Speak Math?**Universal and Stable Precise Expression Truth-Preserving Manipulation**What’s in an Equation, Really?**It’s a statement.**What’s in an Equation, Really?**It’s an ‘is’ statement. 17 - 3 5 = 2**What’s in an Equation, Really?**It’s an ‘is’ statement. 17 - 3 5 ‘is’ 2**Three Types of Equations**Evaluation Equivalence Description**Three Types of Equations**Evaluation Equivalence Description**Evaluation**‘is the numerical value’**Three Types of Equations**Evaluation - ‘is the numerical value’ Equivalence Description**Three Types of Equations**Evaluation - ‘is the numerical value’ Equivalence Description**Equivalence**‘is equivalent to’ ‘can be rewritten as’**Three Types of Equations**Evaluation - ‘has the numerical value’ Equivalence - ‘can be rewritten’ Description**Three Types of Equations**Evaluation - ‘has the numerical value’ Equivalence - ‘can be rewritten’ Description**Description**‘is defined as’ ‘has the form’**Three Types of Equations**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)**Three Types of Equations**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)**More on Descriptive Equations**Functions and Relations Metrics and Statistics**What are Functions?**Mappings from Input to Outputs**response**firing rate frustration dose contrast time What are Functions? Mappings from Input to Outputs**f(x)**y x**f(x)**Still a function y x**f(x)**Not a function y 12 f(50) = ? 63.081 46 x**Types of Equations**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**Types of Equations**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**What are Metrics?**Measures of a Quantity of Interest Often formulaic ‘something-ness’ ‘fat-ness’