# Non-Project Elements ## Attendance * Nothing to turn in here. I'll track attendance and update the Canvas assignment for it weekly. ## Lecture Reflections * I send our codes, lecture boards, and transcription of audio to create our daily notes page. In addition, I also have the LLM create short Canvas quizzes, which we will use to reflect on lecture content outside of class. * 🎯 [MATH 307 — Day 1 Lecture Reflection (Functions, Sampling, Plotting)](https://elearning.mines.edu/courses/79896/quizzes/116507) * [[(307Su26) Day 1 - Functions, sampling, plotting, and manipulation]] * [ 🎯 MATH 307 — Day 2 Lecture Reflection (Plot Refinements & Naive Root Finding)](https://elearning.mines.edu/courses/79896/quizzes/116526) * [[(307Su26) Day 2 - Plot refinements and naive root finding]] * [🎯 MATH 307 — Day 3 Lecture Reflection (Taylor Series & Finite Differences)](https://elearning.mines.edu/courses/79896/quizzes/116547) * [[(307Su26) Day 3 - Taylor series, quadratic root finding, and finite differences]] * [🎯 MATH 307 — Day 4 Lecture Reflection (Taylor Polynomials & Finite Differences)](https://elearning.mines.edu/courses/79896/quizzes/116552) * [[(307Su26) Day 4 - Taylor polynomials and finite-difference approximations]] * [🎯 MATH 307 — Day 5 Lecture Reflection (Taylor Remainder & Second-Derivative Finite Differences)](https://elearning.mines.edu/courses/79896/quizzes/116714) * [[(307Su26) Day 5 - Second-derivative finite differences and the Taylor remainder]] * [🎯 MATH 307 — Day 6 Lecture Reflection (Taylor Remainder Bound, Newton's Method & the Machine Number Line)](https://elearning.mines.edu/courses/79896/quizzes/116715) * [[(307Su26) Day 6 - Root finding and the start of machine precision]] * [🎯 MATH 307 — Day 7 Lecture Reflection (Round-off, Machine Epsilon & Newton's Convergence)](https://elearning.mines.edu/courses/79896/quizzes/116716) * [[(307Su26) Day 7 - Round-off, machine epsilon, and Newton's convergence]] * [🎯 MATH 307 — Day 8 Lecture Reflection (Newton Convergence, FD Error & the Vandermonde Stencil System)](https://elearning.mines.edu/courses/79896/quizzes/116717) * [[(307Su26) Day 8 - Finite-difference stencils by linear systems, noise, and Newton wrap-up]] * [🎯 MATH 307 — Day 9 Lecture Reflection (Just Enough Linear Algebra: Transformations, the Column Picture & the Determinant)](https://elearning.mines.edu/courses/79896/quizzes/116718) * [[(307Su26) Day 9 - Just enough linear algebra - transformations, the column picture, and the determinant]] * [🎯 MATH 307 — Day 10 Lecture Reflection (The Column-Recipe Solver & the Eigenvalue/Eigenvector Problem)](https://elearning.mines.edu/courses/79896/quizzes/116794) * [[(307Su26) Day 10 - Eigenvalues and eigenvectors - a matrix's natural coordinates]] * [🎯 MATH 307 — Day 11 Lecture Reflection (Using Eigen-Data: Covariance & Hessian, and the Start of Quadrature)](https://elearning.mines.edu/courses/79896/quizzes/116828) * [[(307Su26) Day 11 - Eigen-data meets Taylor series, and the start of numerical integration]] * [🎯 MATH 307 — Day 12 Lecture Reflection (The Composite Trapezoid Rule, Coded, and Its Error)](https://elearning.mines.edu/courses/79896/assignments/566163) * [[(307Su26) Day 12 - The composite trapezoid rule, coded, and the start of error analysis]] * [🎯 MATH 307 — Day 13 Lecture Reflection (The Trapezoid Error Bound and the Start of Simpson's Method)](https://elearning.mines.edu/courses/79896/assignments/566908) * [[(307Su26) Day 13 - The trapezoid error bound, and the start of Simpson's method]] * [🎯 MATH 307 — Day 14 Lecture Reflection (Super-Algebraic Convergence, Simpson Coded, and Matrix Multiplication)](https://elearning.mines.edu/courses/79896/quizzes/116937) * [[(307Su26) Day 14 - Super-algebraic convergence, Simpson's method coded, and matrix multiplication]] * 🎯 MATH 307 — Day 15 Lecture Reflection (Adaptive Simpson's Method, and the Start of Initial Value Problems) *(QTI built: `Canvas Quizzes/Day 15/MATH307Su26-Day15-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 15 - Adaptive Simpson's method, and the start of initial value problems]] * 🎯 MATH 307 — Day 16 Lecture Reflection (Euler's Method for Systems) *(QTI built: `Canvas Quizzes/Day 16/MATH307Su26-Day16-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 16 - Euler's method for systems]] * 🎯 MATH 307 — Day 17 Lecture Reflection (Runge-Kutta Methods: RK2 and RK4) *(QTI built: `Canvas Quizzes/Day 17/MATH307Su26-Day17-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 17 - Runge-Kutta methods, RK2 and RK4]] * 🎯 MATH 307 — Day 18 Lecture Reflection (Consolidating IVP Solvers, and Adaptive RKF45) *(QTI built: `Canvas Quizzes/Day 18/MATH307Su26-Day18-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 18 - Consolidating IVP solvers, and adaptive Runge-Kutta-Fehlberg]] * 🎯 MATH 307 — Day 19 Lecture Reflection (Polynomial Interpolation and the Lagrange Form) *(QTI built: `Canvas Quizzes/Day 19/MATH307Su26-Day19-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 19 - Polynomial interpolation and the Lagrange form]] * 🎯 MATH 307 — Day 20 Lecture Reflection (Cubic Splines and Natural Boundary Conditions) *(QTI built: `Canvas Quizzes/Day 20/MATH307Su26-Day20-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 20 - Cubic splines and natural boundary conditions]] * 🎯 MATH 307 — Day 21 Lecture Reflection (Splines, Interpolation, and the Start of Regression) *(QTI built: `Canvas Quizzes/Day 21/MATH307Su26-Day21-Reflection-QTI.zip`; Canvas upload pending)* * [[(307Su26) Day 21 - Splines, interpolation, and the start of regression]] * 🎯 MATH 307 — Day 22 Lecture Reflection (Newton for Systems, the Hessian, and Nested Quadrature) *(QTI built: `Canvas Quizzes/Day 22/MATH307Su26-Day22-Reflection-QTI.zip`; Canvas upload pending)* — **last content day** * [[(307Su26) Day 22 - Newton for systems, the Hessian, and nested quadrature]] ## Workbook The workbook will be updated as we go, and you can find the live pdf, rendered from LaTeX [here](https://www.overleaf.com/read/fhdgfpncsrsy#3d0e9e). They are single-page problems stemming from lecture content that we will collect every two weeks. Some of the earlier ones also have a short Canvas quiz. ### Workbook Problems * 🎯 [Workbook #1 - The geometry of Gaussian functions (quiz)](https://elearning.mines.edu/courses/79896/assignments/564376) * [[MATH307Su26-WB1-Gaussian.pdf]] * [🎯 MATH307 Workbook #2 - Naive Root Finding](https://elearning.mines.edu/courses/79896/quizzes/116531) * [[MATH307Su26-WB2-NaiveRootFinding.pdf]] * [ 🎯 MATH307 Workbook #3 - Code Reuse and Anonymous Functions](https://elearning.mines.edu/courses/79896/quizzes/116532) * [[MATH307Su26-WB3-CodeReuse.pdf]] * [🎯 MATH307 Workbook #4 - Taylor Series of the Gaussian]([CANVAS-LINK-TBD](https://elearning.mines.edu/courses/79896/quizzes/116544)) * [[MATH307Su26-WB4-TaylorGaussian.pdf]] * [🎯 MATH307 Workbook #5 - Finite Differences]([CANVAS-LINK-TBD](https://elearning.mines.edu/courses/79896/quizzes/116546)) * [[MATH307Su26-WB5-FiniteDifference.pdf]] * MATH307 Workbook #6 - Forward second difference * [[MATH307Su26-WB6-SecondDifference.pdf]] · [[(307Su26) Workbook 6 - Forward second difference by undetermined coefficients|companion]] * MATH307 Workbook #7 - Newton's method * [[MATH307Su26-WB7-Newton.pdf]] · [[(307Su26) Workbook 7 - Newton's method by hand|companion]] * MATH307 Workbook #8 - Round-off vs. truncation (finite-difference error tradeoff) * [[MATH307Su26-WB8-FDErrorTradeoff.pdf]] · [[(307Su26) Workbook 8 - Round-off vs truncation, the finite-difference error tradeoff|companion]] * MATH307 Workbook #9 - Solutions as recipes: building $\vec b$ from the columns of $A$ * [[MATH307Su26-WB9-ColumnRecipes.pdf]] · [[(307Su26) Workbook 9 - Solutions as recipes, building b from the columns of A|companion]] * MATH307 Workbook #10 - Matrix transformations of the plane (the fish) * [[MATH307Su26-WB10-FishTransforms.pdf]] · [[(307Su26) Workbook 10 - Matrix transformations of the plane|companion]] * MATH307 Workbook #11 - Eigen-structure and what a transformation does * [[MATH307Su26-WB11-EigenDescribe.pdf]] · [[(307Su26) Workbook 11 - Eigen-structure and what a transformation does|companion]] * MATH307 Workbook #12 - Areas from samples: the composite trapezoid rule * [[MATH307Su26-WB12-TrapezoidGaussian.pdf]] · [[(307Su26) Workbook 12 - Areas from samples, the composite trapezoid rule|companion]] * MATH307 Workbook #13 - Areas from samples: Simpson's rule * [[MATH307Su26-WB13-SimpsonGaussian.pdf]] · [[(307Su26) Workbook 13 - Areas from samples, Simpson's rule|companion]] * MATH307 Workbook #14 - Adaptive quadrature by hand * [[MATH307Su26-WB14-AdaptiveQuad.pdf]] · [[(307Su26) Workbook 14 - Adaptive quadrature by hand|companion]] * MATH307 Workbook #15 - Euler's method by hand: a scalar IVP * [[MATH307Su26-WB15-EulerScalar.pdf]] · [[(307Su26) Workbook 15 - Euler's method by hand, a scalar IVP|companion]] * MATH307 Workbook #16 - Euler's method by hand: a system * [[MATH307Su26-WB16-EulerSystem.pdf]] · [[(307Su26) Workbook 16 - Euler's method by hand, a system|companion]] * MATH307 Workbook #17 - Adaptive Simpson: one accept/subdivide test * [[MATH307Su26-WB17-AdaptiveQuadSqrt.pdf]] · [[(307Su26) Workbook 17 - Adaptive Simpson, one accept-subdivide test|companion]] * MATH307 Workbook #18 - An embedded Euler/RK2 pair for error control * [[MATH307Su26-WB18-EulerRK2Pair.pdf]] · [[(307Su26) Workbook 18 - An embedded Euler-RK2 pair for error control|companion]] * MATH307 Workbook #19 - The Lagrange interpolating polynomial through three points * [[MATH307Su26-WB19-LagrangeQuad.pdf]] · [[(307Su26) Workbook 19 - The Lagrange interpolating polynomial through three points|companion]] ### Workbook Checks * [ 🎯 Workbook check in #1 - Due, July 10th](https://elearning.mines.edu/courses/79896/assignments/564378): Submit your work for workbook problems #1 through #6? * [🎯 Workbook check in #2 - Due, July 24th](https://elearning.mines.edu/courses/79896/assignments/564657): Submit your work for workbook problems #7 through #13 * [🎯 Workbook check in #3 - Due, August 6th](https://elearning.mines.edu/courses/79896/assignments/564658): Submit your work for workbook problems #14 through #20 ## In-Person Workbook Check-ins To confirm that we are indeed human and working through our course material, we will do timed, in-person workbook check-ins on the workbook material. They will be announced with at least 48 hours' notice. They will be graded as complete/full-credit, incomplete w/ requested corrections, and incomplete. If you make reasonable mistakes but know roughly what to do, then you will be asked to make corrections. If the response contains little or no correct work, then you will not. There are currently no deliverables. Prepare through the [[#Workbook Problems]] and prepare the work for the [[#Workbook Checks]]. * [🎯 Timed In-Person Content Checks #1](https://elearning.mines.edu/courses/79896/assignments/565473) * [🎯 Timed In-Person Content Checks #2](https://elearning.mines.edu/courses/79896/assignments/566989) ## Homework Assignments Here we have our longer more complicated single-page homework assignments. * [ 🎯 Homework Assignment #1 - Due, July 8th](https://elearning.mines.edu/courses/79896/assignments/564317) * [[MATH307Su26-HW1.pdf]] * [[HW1-Helper]] * [🎯 Homework Assignment #2 - Due, July 24th](https://elearning.mines.edu/courses/79896/assignments/565926) * [[MATH307Su26-HW2.pdf]] * [[MATH307Su26-HW2-Companion]] * 🎯 [Homework Assignment #3 - Due, July 31st](https://elearning.mines.edu/courses/79896/assignments/567780) * [[MATH307Su26-HW3.pdf]] * [[MATH307Su26-HW3-Companion]] * 🎯 Homework Assignment #4 (final) - Due, August 6th * [[MATH307Su26-HW4.pdf]] * [[MATH307Su26-HW4-Companion]] # Project Elements Projects run through **four milestone check-ins**, one point each: (1) Prospecting & Planning, (2) Implementation & Testing, (3) Completion & Interpretation, and (4) Peer Review, Revision & Editorial. For each check-in, fill out and submit the matching form. * [[Teaching/MATH307/MATH307Su26/Projects_Su26/forms/src/packet.pdf | MATH307Su26 - Project Forms]] ## Projects * [[MATH307Su26 - Multivariate Taylor Series, Hessian Matrices, and Eigendata]] (project handout - updated) * [[MATH307Su26 - Multivariate Taylor Series, Hessian Matrices, and Eigendata (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Multivariate Taylor Series, Hessian Matrices, and Eigendata (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every surface in this project is one line of code. * [[MATH307Su26 - Low Rank Approximations of Images]] (project handout - updated) * [[MATH307Su26 - Low Rank Approximations of Images (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Low Rank Approximations of Images (Verification Table)]] (fill in and submit with Milestone 2) * Data downloads (course website; URLs to be added by Scott): `link_gray.png`, `link_plush.png` * [[MATH307Su26 - Orbital Mechanics and Numerical Integration]] (project handout - updated) * [[MATH307Su26 - Orbital Mechanics and Numerical Integration (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Orbital Mechanics and Numerical Integration (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every orbit in this project is a pair of numbers. * [[MATH307Su26 - Least Squares Approximation for (x,y) Scatter Data]] (project handout) * [[MATH307Su26 - Least Squares Approximation for (x,y) Scatter Data (Milestone Map)|Milestone Map]] (which handout artifact answers each form field) * [[MATH307Su26 - Least Squares Approximation for (x,y) Scatter Data (Verification Table)|Verification Table]] (fill in and submit with Milestone 2) * Data downloads: testData.csv, mystery_dataset.csv, Height_Wingspan_Data.csv (course website; URLs to be added by Scott) * [[MATH307Su26 - Root Finding Methods and the Mathematics of Vibrating Membranes]] (project handout) * [[MATH307Su26 - Root Finding Methods and the Mathematics of Vibrating Membranes (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Root Finding Methods and the Mathematics of Vibrating Membranes (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every function in this project is defined analytically; students supply their own three equations for the finale. * [[MATH307Su26 - Collaborative Filtering and Latent Factor Discovery]] (project handout) * [[MATH307Su26 - Collaborative Filtering and Latent Factor Discovery (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Collaborative Filtering and Latent Factor Discovery (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: the tiny 3x2 survey and the 7x5 ratings matrix are typed inline in the handout and code; the finale uses the student's own mini rating survey. * [[MATH307Su26 - Fat Tails and Black Swans]] (project handout) * [[MATH307Su26 - Fat Tails and Black Swans (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Fat Tails and Black Swans (Verification Table)]] (fill in and submit with Milestone 2) * Data download: eustocks_returns.csv (course website; URLs to be added by Scott) * [[MATH307Su26 - Building the Fourier Transform from Scratch]] (project handout) * [[MATH307Su26 - Building the Fourier Transform from Scratch (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Building the Fourier Transform from Scratch (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: all signals are synthetic and generated in code (the deterministic LCG noise is written out in every language); students construct their own signals for the finale. * [[MATH307Su26 - Chaos, Butterflies, and the Lorenz Equations]] (project handout) * [[MATH307Su26 - Chaos, Butterflies, and the Lorenz Equations (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Chaos, Butterflies, and the Lorenz Equations (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every run is generated from the parameters (sigma, rho, beta) given inline; there is nothing to fetch. * [[MATH307Su26 - From Linear Springs to Nonlinear Pendulums]] (project handout) * [[MATH307Su26 - From Linear Springs to Nonlinear Pendulums (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - From Linear Springs to Nonlinear Pendulums (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every oscillator is a parameter pair given inline (spring m, k or pendulum g, L, theta_0); nothing to fetch. * [[MATH307Su26 - Fourier Regression and Mean Sea Level Change]] (project handout) * [[MATH307Su26 - Fourier Regression and Mean Sea Level Change (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Fourier Regression and Mean Sea Level Change (Verification Table)]] (fill in and submit with Milestone 2) * Data download: `global_mean_sea_level_1993-2024.csv` (course website; URLs to be added by Scott) * [[MATH307Su26 - Regression onto Fourier Basis and Mean Sea Level]] (project handout) * [[MATH307Su26 - Regression onto Fourier Basis and Mean Sea Level (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Regression onto Fourier Basis and Mean Sea Level (Verification Table)]] (fill in and submit with Milestone 2) * Data download: `global_mean_sea_level_1993-2024.csv` (course website; URLs to be added by Scott) * [[MATH307Su26 - Agricultural Interpolation in the Research Literature]] (project handout) * [[MATH307Su26 - Agricultural Interpolation in the Research Literature (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Agricultural Interpolation in the Research Literature (Verification Table)]] (fill in and submit with Milestone 2) * Data download: `crop_data.csv` (course website; URLs to be added by Scott) * [[MATH307Su26 - LivePlotting - Trick Out Your Instrument]] (project handout) * [[MATH307Su26 - LivePlotting - Trick Out Your Instrument (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - LivePlotting - Trick Out Your Instrument (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: the test suite is analytic and lives in the code; the Milestone 4 mystery function is instructor-held, not shipped. * [[MATH307Su26 - Modes by Machine - Boundary Value Problems and the Vibrating String]] (project handout) * [[MATH307Su26 - Modes by Machine - Boundary Value Problems and the Vibrating String (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - Modes by Machine - Boundary Value Problems and the Vibrating String (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads; assigned reading instead: `WaveEquation_v2.0.pdf` (course website; URL to be added by Scott). Read it before Milestone 1. * [[MATH307Su26 - The Price of a Product - Matrix Multiplication, Flop Counts, and the Sparsity Dial]] (project handout) * [[MATH307Su26 - The Price of a Product - Matrix Multiplication, Flop Counts, and the Sparsity Dial (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - The Price of a Product - Matrix Multiplication, Flop Counts, and the Sparsity Dial (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every matrix is generated in code from a fixed seed; the finale matrices are designed by the student. * [[MATH307Su26 - The Illumination Integral and Monte Carlo Rendering]] (project handout) * [[MATH307Su26 - The Illumination Integral and Monte Carlo Rendering (Milestone Map)]] (which handout artifact answers each form field) * [[MATH307Su26 - The Illumination Integral and Monte Carlo Rendering (Verification Table)]] (fill in and submit with Milestone 2) * No data downloads: every sky and light is a formula given inline (the shared LCG random stream is written out in every language); students design their own three skies for the finale. [[Teaching/MATH307/Projects/MATH307Su25 - Projects|MATH307Su25 - Projects]] (In the process of being updated to fit Su26 deliverables.) * Timeline of tools: - Week2 - Root finding, linear algebra, multivariate Taylor series - Week 3/4 - Numerical integration - Week 4/5 - Numerical ODE - Week 5/6 - Interpolation, splines, and regression ## Milestone forms (fill out and submit for each project) Note: In addition to these forms, your final submission will be a zip file containing a working codebase and a <5-minute screen presentation providing an overview of the final outcome. - The forms should help shape what you want to say in the presentation. - Presentations can be done in person if that's easier for the individual. > [!example]- Milestone 1: Prospecting & Planning > ![[form-milestone1-p1.png]] > ![[form-milestone1-p2.png]] > [!example]- Milestone 2: Implementation & Testing > ![[form-milestone2-p1.png]] > ![[form-milestone2-p2.png]] > [!example]- Milestone 3: Completion & Interpretation > ![[form-milestone3-p1.png]] > ![[form-milestone3-p2.png]] > [!example]- Milestone 4: Peer Review, Revision & Editorial > ![[form-milestone4-p1.png]] > ![[form-milestone4-p2.png]] > [!example]- Peer Feedback (reviewer copy; complete two, on classmates' write-ups) > ![[form-peerfeedback-p1.png]] > [!example]- Supporting templates (pseudocode, derivation) > ![[form-pseudocode-p1.png]] > ![[form-pseudocode-p2.png]] > ![[form-derivation-p1.png]] > ![[form-derivation-p2.png]]