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Administrative details:

    1. Contact information and webpage.

    2. Student list and scheduling.
        Please send me email (mth@dam.brown.edu) with
          - name
          - year (freshman, sophomore, ...)
          - concentration
          - other math courses you have taken (Calculus and higher)

    3. Course goals (see Syllabus)

    4. Grading policies and attendance (see Syllabus)

Handout: class outline
   

Administrative details (refer new students to webpage)

Introduction and Overview: (you will not be tested on this material)

    0.1 Three Main Topics
           0.1.1 Differential Equations (see Links for pictures of neurons)
           0.1.2 Probability and Statistics
           0.1.3 Information Theory

Introduction to MATLAB: (see Links)  (today begins material that you will be tested on)

    0.2 MATLAB
           0.2.1 Plotting sinusoids.  TrigDemo.m handout.

Calculus Review in B&H 153 from 7-8:30 pm

           0.2.2 Computing Fibonacci numbers.  FibonacciDemo.m handout.
           0.2.3 A simple differential equation

           0.2.4 Numerical integration

           Homework #1 (due in class Mon., Sept. 26)
           Challenge #1 (optional; turn in with HW#1 for extra credit)

1. Differential equations
   
    1.1 One-dimensional differential equations
          1.1.1 Differential equations and their numerical integration. 

          1.1.1 Differential equations and their numerical integration. 
                   ODE_Demo.m handout.
          1.1.2 Linear equations

          1.1.2 Linear equations

HOMEWORK #1 DUE in class  (3 graphs, MATLAB code, brief explanation)
solutions

          1.1.2 Linear equations
          1.1.3 Some non-linear equations
                   Overhead 1.1.3 #1,  Overhead 1.1.3 #2
          1.1.4 Qualitative analysis

          1.1.4 Qualitative analysis

           Homework #2 (due in class Fri, Oct. 7)
           Challenge #2 (optional; turn in with HW#2 for extra credit)

    1.2 Two-dimensional differential equations
          1.2.1 Examples

          1.2.2 Qualitative analysis
                   1.2.2.1 The phase plane
                   ODE2D_Quiver_Neuron.m handout
                   ODE2D_Trajectory_Neuron.m handout

                   1.2.2.1 The phase plane

          1.2.3 Pairs of linear equations
                   1.2.3.1 Stability analysis
                   Overhead 1.2.3.1 #1,  Overhead 1.2.3.1 #2,  Overhead 1.2.3.1 #3, 
                   Overhead 1.2.3.1 #4,  Overhead 1.2.3.1 #5

          Homework #3 (due in class Mon, Oct. 17 in class)
          Challenge #3 (optional; turn in with HW#3 for extra credit)

                   1.2.3.2 Nullclines

          1.2.4 Pairs of nonlinear equations
                   1.2.4.1 Stability and local analysis
                   1.2.4.2 Two neuron example
                   Overhead 1.2.4.2 #1
                   Neuron Nullcline handout 
                   1.2.4.3 Linear approximations near equilibria

HOMEWORK #2 DUE in class
solutions

                   1.2.4.3 Linear approximations near equilibria
                   Overhead 1.2.4.3 #1,  Overhead 1.2.4.3 #2,  Overhead 1.2.4.3 #3,
                   Overhead 1.2.4.3 #4 

Columbus Day - NO CLASS

                   1.2.4.4 Limit cycles and the Poincare-Bendixson Theorem
                   Overhead 1.2.4.4 #1,  Overhead 1.2.4.4 #2,  Overhead 1.2.4.4 #3, 
                   Overhead 1.2.4.4 #4

          Homework #4 (due in class Fri, Oct. 21)
          Challenge #4 (optional; turn in with HW#4 for extra credit)

Differential Equations review for Exam #1
Differential Equations Practice Exam      Solutions

HOMEWORK #3 DUE in class
solutions

2. Probability and Statistics
    2.1 Probabilities and random variables
          2.1.1 Probability spaces
                   2.1.1.1 Sample spaces
                   2.1.1.2 Events
                   2.1.1.3 Probabilities

                   2.1.1.3 Probabilities
                   Birthday handout

HOMEWORK #4 DUE in class
solutions

                   2.1.1.4 Conditional probabilities

                   2.1.1.4 Conditional probabilities

          2.1.2 Random variables
                   2.1.2.1 Definition
                   2.1.2.2 Probability distributions

3-4 pm Exam Review, CIT 219

Exam #1, Barus & Holley 166, 7-10 pm

                   2.1.2.2 Probability distributions
                   2.1.2.3 Probability densities

return Exam #1

                   2.1.2.3 Probability densities
                   2.1.2.4 Mean, variance and standard deviation

                   2.1.2.4 Mean, variance and standard deviation
                   2.1.2.5 The normal density function
                   2.1.2.6 The binomial distribution

          Homework #5 (due in class Friday, Nov. 11)
          Challenge #5 (optional; turn in with HW #5 (or #6 or #7) for extra credit)

                   2.1.2.6 The binomial distribution

    2.2 Limit laws of probability
          2.2.1 The Law of Large Numbers (LLN)
                   2.2.1.1 Independent random variables
                   2.2.1.2 Identically distributed random variables

                   2.2.1.3 LLN
                   LLN_Uniform.m handout,  LLN_UniformSq.m handout

          2.2.2 The Central Limit Theorem (CLT)
                   2.2.2.1 Examples (with MATLAB)
                   2.2.2.2 Standardized sums
                   SampleUniformSums.m handout,  SampleUniformSqSums.m handout

HOMEWORK #5 DUE in class
solutions

                   2.2.2.3 CLT
                   CLT_test handout

          Homework #6 (due in class Friday, Nov. 18)

    2.3 Hypothesis Testing
          2.3.1 Basic elements of a hypothesis test
                   2.3.1.1 Main idea
                   2.3.1.2 Definitions
                   2.3.1.3 Critical region and significance level

                   2.3.1.3 Critical region and significance level
          2.3.2 Examples
                   2.3.2.1 Voter preference
                   2.3.2.2 Tricky Baby Josephine

HOMEWORK #6 DUE in class
solutions

                   2.3.2.3 Approximate tests using CLT
                   2.3.2.4 Extreme fishing

          Homework #7 (due by noon Tuesday, Nov. 29, in my box)

Probability and Statistics review for Exam #2
Probability and Statistics Practice Exam    Solutions

Thanksgiving recess - NO CLASS

Thanksgiving recess - NO CLASS

3. Information Theory
    3.1 Measures of information / uncertainty
          3.1.1 "Twenty questions"
          3.1.2 Bits

3-4 pm Problem Session, CIT 219

HOMEWORK #7 due in my box in 182 George St (1st floor) at 12:00 noon
solutions

          3.1.2 Bits

3-4 pm Exam Review, CIT 219

Exam #2, Barus & Holley 166, 7-10 pm

return Exam #2

          3.1.3 Entropy

          Homework #8  (due in class Friday, Dec. 9)

          3.1.4 Lossless coding
                   3.1.4.1 Codes
                   3.1.4.2 Prefix codes
                   3.1.4.3 Optimal prefix codes
                   link to Claude Shannon handout

    3.2 Measures of mutual information
          3.2.1 Pairs of random variables
                   3.2.1.1 Joint probability distributions
                   3.2.1.2 Joint entropies
                   3.2.1.3 Conditional probability distributions

HOMEWORK #8 Due in class
solutions

                   3.2.1.4 Conditional entropies
          3.2.2 Mutual information
                   Summary handout
 
          3.2.3 An application in neuroscience

          Fill out class surveys.

          Homework #9  (due by 4pm Wednesday, Dec. 14, in my box)

Problem session  7-8:30 pm  Barus & Holley 158

HOMEWORK #9 due in my box in 182 George St (1st floor) at 4:00 pm
solutions

Exam review  7-8:30 pm  Barus & Holley 158

EXAM #3  9:00 am  Barus & Holley 155