Week  Date  Topic/Materials/Tasks 
1 
Mon Aug 24 
 Introduction, syllabus, etc.
 Get set up on the
Sagemath Cloud:
 Use Firefox (or Chrome), not Internet Explorer.
 Sign up for a free account using your real name
and your University email address (@ohio.edu). Sign
in.
 Click on "Help" in the upper left and read about it.
 Look for a project in your account titled with your
name. I created this and shared it with you. Your
submissions as an individual, such as your
biography, go here.
 Look for a project "NumericalClass". I
will put things here for the whole class to use.
 Do your Biographical Survey

Wed Aug 26 
 Find your partner for this week's tasks and
journal, and sit next to them. (Look in
NumericalClass/partners.sagews to find out who your
partner is.)
 Look for a project shared with your partner. You
will submit your journal using this project.
 One of you upload the journal sample to this
shared project. You can then both edit it.
 Play with this journal and make it into your own
journal. A cell with code is run by entering it, holding
the "shift" key and hitting the "enter" (return) key. A
cell with pretty text can be made using either html
or markdown. (You
can see how a cell with text was made by selecting it
and hitting the button in the upper left that looks like
an eye with a slash through it.) (Note that if a cell
has too many lines in it, then it does not work, or at
least does not produce output.)
 Skim the tutorial Guided
Tour and try some things in your journal.

Thu Aug 27 8am Biographical survey (counts as a
journal) due. (No 5600 exploration due.) 
Fri Aug 28 
 Read about Taylor's
theorem. In your journal, state and prove Taylor's
theorem with Lagrange form of the remainder. Be sure to
cite your source(s).
 To learn about some functions you likely will use today,
do: var?, derivative?, plot?, points?, factorial?
 Copy the sage cell on Taylor
Series into your journal. Modify it so that it gives
the Lagrange form of the remainder. Make it plot the
function and the Taylor Polynomial.
 For the function \(f(x)=\cos(x)\), we can easily
bound \(f^{(k+1)}(x)\) and so can easily bound the
Lagrange form of the remainder. For this function,
illustrate graphically that the actual remainder
satisfies the bound you obtained.

2 
Mon Aug 31 

Tue Sep 1 8am journal for Aug 2628 draft due;
I will make comments and corrections but not grade it. 
Wed Sep 2 
 Find your partner for this week's tasks and journal,
and sit next to them.
 Read the Good Problems handout on
Flow. All future journals will have some points for
demonstrating the flow skills.
 In deciding how much to write, a good standard is:
If someone reads only the text (none of the code) in
your journal, it should still make sense to them.
 To learn about some functions you likely will use today,
do:
expand?, show?, point?
 Read about Interpolation. In
a few sentences, summarize what it is.
 Read about Polynomial
interpolation. In a few sentences, summarize what it
is. State and prove the polynomial interpolation error/remainder,
assuming the function is sufficiently differentiable. Be sure to
cite your source(s).
 Read about the Lagrange
Polynomial. In a few sentences, summarize what it
is. Read the example,
reproduce it (making sage do most of the work), and plot
the result to show it interpolates as desired.

Thu Sep 3 8am journal for Aug 2628 (and
5600 exploration) due. 
Fri Sep 4 
(drop deadline)
 Upload the rating file
to your (individual) project.
In it rate your partner from last week.
 Read about lists, the for statement, range, defining functions
 Make a function that inputs a list of points
\([x_0,\dots,x_{n1}]\) and an index \(k\) with \(0\le k
\le n1 \) and outputs the Lagrange interpolating
polynomial that is 1 at \(x_k\) and 0 and the other
\(x_i\).
 Make a function that inputs a list of points
\([x_0,\dots,x_{n1}]\) and values
\([y_0,\dots,y_{n1}]\) and outputs the interpolating
polynomial that passes through all \((x_i,y_i)\). It
should use the function you made above.
 Test your function on the example
we used earlier.

3 
Mon Sep 7 
Labor day holiday, no class 
Wed Sep 9 
 Find your partner for this week's tasks and
journal, and sit next to them.
 One of you create a project in which to work on your
journal, using the naming convention "3 Name1 and
Name2". Set the other person and me as collaborators on
that project.
 Read the Good Problems handout on
Introductions and Conclusions. All future journals
will have some points for including an introduction and
a conclusion.
 Read about Rate
of convergence.
 Read about Newton's
Method. State and prove the quadratic convergence of
Newton's method (under certain assumptions).
 Make a function that inputs \(f\), \(x_0\), and
\(k\) and outputs a list of the results of performing
Newton's method \(k\) times starting at \(x_0\).
(Use N() on the input \(x_0\) to make sure the
computation is numerical
rather than symbolic.)
 Use your function to demonstrate that Newton's
method has quadratic convergence when applied
to \(f(x)=x^22\) starting at \(x_0=3\).

Thu Sep 10 8am journal for Sep 24 (and
5600 exploration) due. 
Fri Sep 11 
 Rate your partner from last week.
 Read about the Secant
method (see also here). State and prove the convergence rate of
the secant method (under certain assumptions).
 Make a function that inputs \(f\), \(x_0\), \(x_1\), and
\(k\) and outputs a list of the results of performing
the secant method \(k\) times starting with \(x_0\)
and \(x_1\).
 Use your function to demonstrate that the secant
method has the claimed rate of convergence when applied
to \(f(x)=x^22\) starting with \(x_0=3\) and \(x_1=2\).

4 
Mon Sep 14 
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Read the Good Problems handout on
Logic. Starting with this journal, you need to make
your logic clear and use logical connectives.
 Read about Numerical
Integration. In a few sentences, summarize what it
is.
 Read about the Trapezoid(al)
Rule. Write a (sage/python) function that inputs a
function \(f\), a number \(a\), and a number \(b\) and
outputs the trapezoidal approximation to \(\int_a^b f(x)
dx\). (Do the singleinterval trapezoidal rule, not the
composite rule.)
 Write similar functions for the (singleinterval) midpointrule
and Simpson's
rule.
 Each of these three methods is
supposed to be exact for polynomials up to some degree
and not further. For each method, state the supposed
exactness degree and use your functions to demonstrate
that this degree is correct.

Tue Sep 15 8am journal for Sep 911 (and
5600 exploration) due. 
Wed Sep 16 
 Rate your partner from last week.
 Read about NewtonCotes
formulas. In a few sentences, summarize what they
are. (Also read about their error
analysis.)
 Write a function that inputs a function \(f\),
numbers \(a\), \(b\), and \(n\), and a (sage/python)
function \(R\)
like the ones you made Monday, and outputs an
approximation to \(\int_a^b f(x) dx\) using a
composite rule with \(n\) intervals and the method
\(R\) on each interval.
 Test your function using the three methods from
Monday on the integral \(\int_1^{3/2} x^2 \ln(x) dx\).
Which method performs best?
Does this agree with their theoretical performance?
Explain your conclusions.

Fri Sep 18 
 Determine the values of \(c_1\), \(c_2\), and
\(x_2\) that make the approximation
\(\int_0^2 f(x)\,dx\approx c_1 f(0)+ c_2f(x_2)\)
as accurate as possible. Validate your choices
with a test.

5 
Mon Sep 21 
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Familiarize yourself with NumPy.
 Do "import numpy" and "from numpy.random import randn"
and then use randn to generate a random scalar \(a\),
and three random \(10\times 10\) matrices \(A\), \(B\),
and \(C\).
 Do "from numpy import identity,zeros,dot"
and use these to create the identity
matrix \(I\) and zero matrix \(O\).
 Read about Norm
and Matrix
norm. From numpy.linalg import norm.
To test an equality like \(A=B\), we can check
\(\AB\\approx 0\).
 Test the following equalities
 \(O+A=A\)
 \(A+B=B+A\)
 \(A+(B+C)=(A+B)+C\)
 \(IA=A\)
 \(AB=BA\)
 \(A(BC)=(AB)C\)
 \(a(B+C)=aB+aC\)
 \(A(B+C)= AB+AC\)

Tue Sep 22 8am journal for Sep 1418 (and
5600 exploration) due. 
Wed Sep 23 
 Rate your partner from last week.
 Read about eigenvalues and eigenvectors. In a few sentences, summarize what they are.
 From numpy.linalg import eig. Create
a random \(10\times 10\) matrix \(A\) and compute its
eigenvalues and eigenvectors using eig. Run a test to
verify that they really are eigenvalues and
eigenvectors.

Fri Sep 25 
 Read about invertible
matrices. In a few sentences, summarize what they
are.
 From numpy.linalg import inv. Create
a random \(10\times 10\) matrix \(A\) and compute its
inverse using inv. Run a test to verify that the inverse
satisfies the properties that it is suppose to.

6 
Mon Sep 28 
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Read about the Singular Value Decomposition (SVD).
State its definition.
 Generate a random \(10\times 7\) matrix \(A\), compute its
SVD using numpy.linalg.svd,
and run tests to show the results satisfy the definition
of the SVD.
 Read about the (MoorePenrose) pseudoinverse. State its definition.
 Use numpy.linalg.pinv
to compute the psuedoinverse and run tests to show it
satisfies the definition.
 Use the SVD of \(A\) produced by svd() to construct
the psedoinverse of \(A\) and compare with the one
produced by pinv().

Tue Sep 29 8am journal for Sep 2125 (and
5600 exploration) due. 
Wed Sep 30 
 Rate your partner from last week.
 Read about Systems
of linear equations
 Create a random \(10\times 10\) matrix \(A\) and random
\(10 \times 1\) vector \(y\). Compute \(b = Ay\) and then use
numpy.linalg.solve to solve
\(Ax=b\) for \(x\). Compare \(x\) and \(y\).
 Let \(B\) be the \(10\times 9\) matrix containing
the first 9 columns of \(A\). Use the pseudoinverse
\(B^+\) to
"solve" \(Bz=b\) for \(z\). Compare \(z\) with \(y\) and
\(Bz\) with \(b\). How should we interpret \(z\)?
How can we test that \(z\) is correct?

Fri Oct 2 
Reading day holiday, no class 
7 
Mon Oct 5 
 MATH 4600 students:
 Sometime this week, browse SIURO.
 MATH 5600 students:
 For your exploration due next week:
 Read a paper from SINUM
or SISC.
 Write a paragraph or two summarizing (in your
own words) what the paper is about.
 Do some small sage/python computation somehow
related to the paper.
 Include the full citation to the paper in your
journal and upload a copy of the paper.
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Read about Numerical
ordinary differential equations.
 Define what it means for a method to be "consistent".
 Define what it means for a method to be "convergent".
 Define what it means for a method to have "order p".
 Read about the Euler
method. Prove that the Euler method is consistent.
 Make a function that does one step of the Euler
method. The inputs are
 \(f\), which defines the differential equation
\(\dot{\mathbf{x}} = f(\mathbf{x},t)\);
 \(\mathbf{x}_0\), the initial value of \(\mathbf{x}\);
 \(t_0\), the initial value of \(t\); and
 \(h\), the step size in \(t\).
The output is the approximate value of \(\mathbf{x}(t_0+h)\).
 Make a function of the same form that does one step
of the (explicit) Midpoint
Method.
 Validate your codes by reproducing the Euler and
Midpoint parts of these vector
form exercises.

Tue Oct 6 8am journal for Sep 2830 (and
5600 exploration) due. 
Wed Oct 7 
 Rate your partner from last week.
 Fix \(\mathbf{x}_0=2\), \(t_0=0\), and
\(h=1/3\). Test your Euler and Midpoint codes versus the
exact solution for the ODEs defined by
\(f(\mathbf{x},t)=0\), \(f(\mathbf{x},t)=1\),
\(f(\mathbf{x},t)=t\), and \(f(\mathbf{x},t)=t^2\). What
do the results indicate about the consistency,
convergence, and/or order of these two methods?
 Fix
\(\mathbf{x}_0=\left[\begin{array}{c}1\\0\end{array}\right]\),
\(t_0=0\), and \(f(\mathbf{x},t)=
f\left(\left[\begin{array}{c}x_1\\x_2\end{array}\right],t\right)
=\left[\begin{array}{c}x_2\\x_1\end{array}\right]\).
Test your Euler and Midpoint codes versus the exact
solution as \(h\rightarrow 0^+\). What do the results
indicate about the consistency, convergence, and/or
order of these two methods?

Fri Oct 9 
 Read about RungeKutta
methods. Write a function similar to your Euler and
Midpoint codes that implements "the" RungeKutta 4
method. Run tests on it like you did on Wednesday.
What do the results
indicate about the consistency, convergence, and/or
order of the RK4 method?

8 
Mon Oct 12 
 MATH 4600 students:
 Browse SIURO more.
 MATH 5600 students:
 For your exploration due next week, explore another paper from SINUM
or SISC.
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Make a function that does several steps of an ODE method.
The inputs should be:
 \(f\), which defines the differential equation
\(\dot{\mathbf{x}} = f(\mathbf{x},t)\);
 \(\mathbf{x}_0\), the initial value of \(\mathbf{x}\);
 \(a\), the initial value of \(t\);
 \(b\), the final value of \(t\);
 \(n\), the number of steps to take in \(t\) to get from
\(a\) to \(b\); and
 \(M\), a function that does a single ODE step,
like the ones you made last week.
The outputs should be:
 \(T\), an array with the values of \(t\) used and
 \(X\), an array with the computed values of \(x\) at
those values of \(t\).
 Validate your code on the vector
form exercises.
 Fix
\(\mathbf{x}_0=\left[\begin{array}{c}1\\0\end{array}\right]\),
\(a=0\), \(b=2\pi\), and \(f(\mathbf{x},t)=
f\left(\left[\begin{array}{c}x_1\\x_2\end{array}\right],t\right)
=\left[\begin{array}{c}x_2\\x_1\end{array}\right]\).
Test your Euler, Midpoint, and RK4 codes versus the exact
solution as \(n\rightarrow \infty\). What do the results
indicate about the consistency, convergence, and/or
order of these methods?

Tue Oct 13 8am journal for Oct 59 due. 
Wed Oct 14 
 Rate your partner from last week.
 Read about adaptive stepsize.
 Make a function that adaptively chooses the step size.
The inputs should be
 \(f\), \(\mathbf{x}_0\), \(a\), \(b\), and \(M\)
as above;
 \(M_2\), a higherorder method than \(M\); and
 \(\epsilon\), a target accuracy.
The outputs should be:
 \(T\), an array with the values of \(t\) used,
with last entry \(b\), and
 \(X\), an array with the computed values of \(x\) at
those values of \(t\).
At each step it should try both \(M\) and \(M_2\) with
the current \(h\). If the difference is more than
\(\epsilon/(h(ba))\) then reject that step and try
again with \(h\mapsto h/2\); if it is less than
\(\epsilon/(h(ba))\) then take that step and consider
increasing \(h\). (Note that this algorithm is
different than in the adaptive
stepsize description.)
 Fix \(x_0=1\), \(a=0\), \(b=1\), and
\(f(x,t)=\sin(10\pi t^2(32t))(60\pi t(1t))\), which
has exact solution \(x(t)=\cos(10\pi t^2(32t))\). Test
your function using Euler for \(M\), Midpoint for
\(M_2\), and \(\epsilon=10^{3}\). Plot the output (as
points) and the exact solution to demonstrate that you
have a good approximation and that \(h\) is
adapting.

Thu Oct 15 8am 5600 exploration about a paper due. 
Fri Oct 16 
Catch up. 
9 
Mon Oct 19 
 Find your partner for this week's tasks and
journal, and sit next to them.
 Read about Numerical
Differentiation and these examples
on determining the coefficients and order for a method.
 Determine the coefficients \(a_1\), \(a_2\), and
\(a_3\) so that \(f'(x_0)=\frac{a_1f(x_0)+a_2f(x_0+h)
+a_3f(x_0+2h)}{h} +\mathcal{O}(h^p)\) for the largest
possible \(p\).
 Determine the coefficients \(b_1\), \(b_2\), and
\(b_3\) so that \(f''(x_0)=\frac{b_1f(x_0)+b_2f(x_0+h)
+b_3f(x_0+2h)}{h^2} +\mathcal{O}(h^q)\) for the largest
possible \(q\).
 Write functions to implement your formulas. Test
them on \(f(x)=e^{3x}\) at \(x_0=2\) using \(h=2^{i}\)
for \(i=0,1,2,\dots,15\) to verify the \(p\) and
\(q\) you determined above.

Tue Oct 20 8am journal for Oct 1216 due. 
Wed Oct 21 
 Rate your partner from last week.
 Read about Loss
of Significance.
 Repeat your test from Monday but let \(i\) go up to
31 and describe the results. Make loglog plots
showing the errors as functions of \(h\).

Thu Oct 22 8am 5600 exploration about a paper due. 

Fri Oct 23 
 Upload talktemplate.tex and OHIOCLR.pdf. Modify
talktemplate.tex into a short but coherent talk on
Numerical Differentiation and Loss of Significance,
using your results from Monday and Wednesday. Do the
first derivative case only. Include the graph you made
Wednesday. Your main product today is the resulting
slides; in your journal comment briefly on problems you
encountered, cool things you learned, etc.

10 
Mon Oct 26 
Think about what paper you want to
do for your final project. The goal of the project is to
validate (or refute) the analysis and numerical results
presented in the paper.
Here are some aspects to consider:
 It is best if the paper is from SIURO for 4600 students or SINUM
or SISC for 5600 students.
 It is best if the paper is recent, so the method in
it is neither wellestablished nor discredited.
 Avoid papers that give subtle improvements for
complicated problems. They likely need too much
coding.
 Look for a paper whose numerical results are based on
simpletoreproduce test problems. If it uses any data
sets, make sure they are publically available.
 MATH 4600 students:
 Decide if the three of
you will do the project together, two will be together
and one alone, or all three alone. I will adjust my
expectations based on the number of people working on
the project. By Friday let me know the grouping and
propose the paper(s) you want to work on.
 MATH 5600 students:
 For your exploration
due Thursday, decide on the paper you want to work
on. It can be one you did an exploration on or a new
one. Explain why you think this a good choice for the
project. I will either accept it or tell you to look for another.

Tue Oct 27 8am journal for Oct 1923 due. 
Wed Oct 28 
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Rate your partner from last week.
 (Re)read about Matrix
norm. State the formula for the matrix norm induced
by \(\\cdot\_2\) in terms of the singular values.
 Write a function that inputs a matrix \(A\) and
outputs its matrix norm induced by \(\\cdot\_2\).
 Read about Condition
Number. Summarize in your own words. State the
relationship between condition number and the error in
solving a linear system. State the formula for the
condition number of a matrix with respect to
\(\\cdot\_2\) in terms of the singular values.
 Write a function that inputs a matrix \(A\) and
outputs its condition number with respect to
\(\\cdot\_2\).
 Write a function to construct a randomlooking
square matrix with specified size, norm, and condition
number. The inputs should be:
 \(m\), the size of the matrix;
 \(n\), the norm of the matrix; and
 \(k\), the condition number of the matrix.
The output is \(A\), which is a \(m\times m\) matrix
with norm \(n\) and condition number \(k\).
 Validate your three functions against each other.

Thu Oct 29 8am
5600 project proposal (counts as an exploration) due. 
Fri Oct 30 
(drop deadline with WP/WF)
 Write a function to test how the error in solving a
linear system depends on \(m\), \(n\), and \(k\), as
used above. The inputs are \(m\), \(n\), and \(k\). The
function should create \(A\) with that size, norm, and
condition number; create a \(m\times 1\) vector \(y\);
compute \(b=Ay\); solve \(Ax=b\) for \(x\), and return
the relative error between \(x\) and \(y\).
 State the theoretical dependence of that relative
error on \(m\), \(n\), and \(k\). Use your function to
test this dependence.

11 
Mon Nov 2 
 Look at NumericalClass/ratinganalysis.sagews for how
the ratings of partners will be used to adjust journal
grades. If you can think of a better way to make
adjustments, please suggest it.
 Work on your
project.

Tue Nov 3 8am journal for Oct 2830 due. 
Wed Nov 4 
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal.
 Rate your partner from last week.
 Read the Good Problems handout on
Graphs. Starting with this journal, pay extra
attention to titles, labels, and legends on your graphs.
 Read about Analysis of algorithms.
 Suppose \(A\) and \(B\) are \(k\times k\)
matrixes. Determine the number of multiplications
needed to compute \(C=AB\), as a function of \(k\).
 Read about the python timeit
library. Sage has its own timeit function, so to get the
python one, do "import timeit as pytimeit".
 Run the code:
import timeit as pytimeit
s = lambda k : "from numpy import dot; from numpy.random import randn; A=B=randn("+str(k)+","+str(k)+")"
ks = [2**j for j in range(10)]
T = [pytimeit.timeit("C=dot(A,B)",setup=s(k),number=2**13/k)/(2**13/k) for k in ks]
plot_loglog(points(zip(ks,T)))
Explain what it does. Analyze T further to determine
how well it agrees with your analysis on the number of
multiplications. Produce at least one illustrative
graph (with title, axis labels, and legend).
 Perform a similar analysis for multiplying a \(k\times k\)
matrix on a \(k\times 1\) vector.

Thu Nov 5 8am
5600 exploration due. It can (should) be related to your project.

Fri Nov 6 
 Read about the Fast
Fourier transform. What is the point of it?
 Read about numpy.fft.
 Run tests on numpy.fft.fft
similar to those you did for matrixvector
multiplication. How well do they agree with the
theoretical results?

12 
Mon Nov 9 
 How long should the final project presentations be?
Nominally, we have (3 classes)(55 minutes/class)/(16
presentations) = 10.5 minutes/presentation but
transition costs will reduce that to 8 minutes. If we run
past the end of class then they could be longer.
 Work on
your project.

Tue Nov 10 8am journal for Nov 46 due. 
Wed Nov 11 
Veterans day holiday, no class 
Thu Nov 12 8am
5600 exploration due. It can (should) be related to your project.

Fri Nov 13 
 Rate your partner from last week.
 Find your partner for this week's tasks and
journal, sit next to them, and set up a project for
your journal. You will keep this partner next week.
 Read about Stiff
equations. What are they?
 The description above has a motivating example of
the ODE \(\dot{x}=15x\) with \(x_0=1\) on \(t\in
[0,1]\) and shows what the Euler method does for
\(h=1/4\) and \(h=1/8\). Apply your Euler, midpoint, and
RK4 programs from Week 7 using your (nonadaptive) ODE
stepping program from Week 8 to this ODE. Produce a plot
with the exact solution these three methods using
\(h=1/4\) and a second plot using \(h=1/8\). Interpret
the results.

13 
Mon Nov 16 
 Notice the presentation and report guidelines at the
end of the schedule.
 Work on your project.

Wed Nov 18 
 The second order ODE
\(\ddot{x}+1001\dot{x}+1000x=0\) with \(x(0)=1\) and
\(\dot{x}(0)=0\) has exact solution
\(x(t)=\frac{1}{999}\exp(1000t)+\frac{1000}{999}\exp(t)\). Plot
this function on \([0,1]\) and observe how nicely it
behaves.
 It is equivalent to the firstorder system
\(\dot{\mathbf{x}} = \left[\begin{array}{cc} 0 & 1 \\
1000 & 1001\end{array}\right] \mathbf{x}\) with
\(\mathbf{x}_0 =\left[\begin{array}{c} 1 \\
0\end{array}\right]\). Run your convergence test from
Week 8 on this ODE on \(t\in [0,1]\) using Euler,
midpoint, and RK4; measure error with respect to the
exact solution \(x(t)\) above (not the exact
\(\mathbf{x}(t)\)).
Interpret the results. How small does
\(h\) need to be to get error less than \(1/10\)?

Thu Nov 19 8am rough draft of final project due.
For 5600 students counts as an exploration. 
Fri Nov 20 
 Coding tips:
 Pull out chunks as their own functions/ subroutines and
test them separately.
 Put a comment before each line saying what it is
supposed to do and what type of object (array, list
of k vectors, ...) it creates. Check the comments
versus the algorithm to make sure what they say
agrees with what is supposed to happen. Then check
the code line against the comment to make sure the
code does what the comment says it does.
 Read about Explicit
and implicit methods. State the distinction between
them.
 Make a function that does one step of the Backward
Euler method. Have the same inputs and outputs as
your Euler method did in Week 7. To solve the equation
for the next value of \(x\), use scipy.optimize.root.
 Repeat your tests from Wednesday using your Backward
Euler function. Compare and contrast with the results
from Wednesday.

14 
Mon Nov 23 
 Rate your partner from last week.
 Look in NumericalClass/partners.sagews for the
presentation order.
 Work on your presentation.

Tue Nov 24 8am journal for Nov 13, 18, and 20 due.
(No 5600 Exploration this week or next.)

Wed Nov 25 
Thanksgiving holiday, no class 
Fri Nov 27 
Thanksgiving holiday, no class 
15 
Mon Nov 30 
Presentations:
 Must be at least 10 and at most 15 minutes long.
 Must use \(\LaTeX\) slides in the beamer class.
 Aim for half the presentation to explain to the
class what the paper is about and half to show what
you did.
 Worth 10% of your project grade.
 You will rate each other

Wed Dec 2 
More presentations 
Fri Dec 4 
More presentations 
16 
Wed Dec 9 
Final Exam 12:202:20 pm
(virtual, your presence is not required).
 Presentation slides due.
 You can improve them based on feedback from your
presentation.
 Worth 10% of your project grade.
 Project report due. The grading is based on the
following rubric:
 Introduction (5%)
 Conclusion (5%)
 Logical Connectives (5%)
 Flow (5%)
 Graphs (5%)
 References, citations, quoting, attribution (5%).
These points are for properly attributing bits from
the paper that your project is on. Improperly
taking material from other sources (including
Wikipedia) will be considered academic misconduct.
 Your analysis of their analysis (20%). Summarize
the central points of what they tried to do. Walk
through the main algorithm and analysis. Expand
and fill in details on some small piece. (Limit
your analysis to what is in the paper; you do not
need to verify statements using other
sources. Ignore side issues, generalizations, and
special cases when possible.)
 Your reproduction of their numerical results
(30%). Since the amount and difficulty of the
numerical results in the papers varies widely,
please consult with me on which parts to reproduce.
