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

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

  2. MathToolsforNeuroscience Greg Ilana

  3. Today: • Introduction • Equations are your friends • <break> • Remember Calculus?

  4. The two questions: What am I going to learn? Math a foreign language: Why should I care? Because you will be tested on it.

  5. 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

  6. 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

  7. 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

  8. Why do we care? Analysis Description

  9. Why do we care? Statistics Description

  10. Why do we care? Statistics Modeling

  11. Who is the course for? Survey Review

  12. What are the Goals? Broad Introduction Intuition & Comfort Solid Statistics Read Any Paper Propose Novel Analyses

  13. What are the Goals? I. The Basics II. Probability and Statistics III. Advanced Topics

  14. But I’m Not A Systems Neuroscientist Cognitive Neuroscience Molecular Genetics

  15. Technical Stuff Website

  16. Technical Stuff mathtools.stanford.edu

  17. Technical Stuff mathtools.stanford.edu Problem Sets

  18. Technical Stuff mathtools.stanford.edu Problem Sets Survey & Sign Up Sheet Lecture Notes Feedback

  19. Equations are Your Friends How to Speak Math Your Pet Equation

  20. Why Speak Math? Universal and Stable Precise Expression Truth-Preserving Manipulation

  21. What’s in an Equation, Really? It’s a statement.

  22. What’s in an Equation, Really? It’s an ‘is’ statement. 17 - 3  5 = 2

  23. What’s in an Equation, Really? It’s an ‘is’ statement. 17 - 3  5 ‘is’ 2

  24. Three Types of ‘is’

  25. Three Types of Equations Evaluation Equivalence Description

  26. Three Types of Equations Evaluation Equivalence Description

  27. Evaluation ‘is the numerical value’

  28. Three Types of Equations Evaluation - ‘is the numerical value’ Equivalence Description

  29. Three Types of Equations Evaluation - ‘is the numerical value’ Equivalence Description

  30. Equivalence ‘is equivalent to’ ‘can be rewritten as’

  31. Three Types of Equations Evaluation - ‘has the numerical value’ Equivalence - ‘can be rewritten’ Description

  32. Three Types of Equations Evaluation - ‘has the numerical value’ Equivalence - ‘can be rewritten’ Description

  33. Description ‘is defined as’ ‘has the form’

  34. 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)

  35. 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)

  36. More on Descriptive Equations Functions and Relations Metrics and Statistics

  37. What are Functions? Mappings from Input to Outputs

  38. response firing rate frustration dose contrast time What are Functions? Mappings from Input to Outputs

  39. What are Functions?

  40. f(x) y x

  41. f(x) Still a function y x

  42. f(x) Not a function y 12 f(50) = ? 63.081 46 x

  43. Functions come in all flavors

  44. Functions come in all flavors

  45. Functions come in all flavors

  46. 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

  47. 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

  48. What are Metrics? Measures of a Quantity of Interest Often formulaic ‘something-ness’ ‘fat-ness’