# Course Vitals **Description**: An introduction to modeling and communication in mathematics. A writing intensive course providing a transition from the core math sequence to the upper division AMS curriculum. Topics include a variety of mathematical and statistical modeling techniques. Students will formulate and solve applied problems and will present results orally and in writing. In addition, students will be introduced to the mathematics software that will be used in upper-division courses. Prerequisite: MATH201, MATH213, MATH225; CSCI128. - **Course Student Learning Outcomes**: - General: - Formulate and investigate mathematical and statistical models - Identify multiple types of models and techniques - Communicate the results of a modeling study in writing and orally - Specific: - Define the process of mathematical modeling and highlight specific examples judged to be relevant to applied mathematics and/or statistics.  - Deconstruct and annotate developed mathematical models for the purposes of summarizing and explaining their assumptions, methods, and conclusions.  - Collaborate with others to choose, build and defend mathematical models based on arguments associated with their validity and commentary on their real-world applicability. - Review, extend and contextualize pre-requisite coursework # Lecture Notes - [[MATH310F26(Day 1) - Instructor information and introduction to the course]] - [[MATH310F26_WB1.pdf|Workbook1 - Logistic Growth w/ Constant Rate Harvesting(pdf)]] - [[MATH310F26(Workbook 1 Companion) - The phase line and what f-prime tells you]] - [[MATH310F26(Day 2) - Modeling in your own words, and two videos]] - [[MATH310F26(Day 3) - A dint on least squares, and the two videos]] - [[MATH310F26(Day 4) - Differencing, the regression run, and a name for the pipeline]] - [[MATH310F26(Day 5) - The Dirac delta, and the idea of a distribution]] - [[MATH310F26(Day 6) - The derivative of a step, distributionally]] - [[MATH310F26(Day 7) - The Fourier transform, intuitively]] - [[MATH310F26(Day 8) - The spectrum of a pure tone]] - [[MATH310F26(Day 9) - The rectangular pulse]] - [[MATH310F26(Day 10) - Hearing the Fourier transform]] # Project Ideas and Reading Directions Curated entry points for the project threads that have emerged from your questions. Each track says what the reading is, why it fits the course, which parts to read for which question, and how to turn it into a model review or a modeling project. - [[MATH310F26 - Reading Track - Stochastic Differential Equations]]. Five notes from random walks to Itô's formula. For anything random in time. Prices, decisions, crowds, noisy populations. - [[MATH310F26 - Reading Track - Mathematical Finance]]. Petters and Dong through the Mines library. Vocabulary first, then binomial trees as random walks, then geometric Brownian motion. - [[MATH310F26 - Reading Track - Oscillators, Linear and Nonlinear]]. Three notes from last year. The mass-spring system with honest numerics, then the Duffing oscillator and what nonlinearity changes. Python, R, and MATLAB side by side. - [[MATH310F26 - Reading Track - Why You Hear What You Hear]]. Heller's book on sound, music, and psychoacoustics. For the sound, speech, and music questions, and a second exposure to Fourier. # Applets Interactive pages — play in the browser, hear the mathematics (an assignment built on these is coming): - [[Fourier Series]] — build waves from harmonics, draw your own periodic function, and listen to every term - [[Fourier Transforms]] — the rect ↔ sinc pair, the pulse train, duality as click vs. thump, the 2-D bar, and the image DFT (upload your own picture) # Workbook One workable problem per lecture, collected monthly (**WB**), with a short correctable check every two weeks (**WC**). Each workbook is a one-page problem sheet; companion pages walk through the method on a *different* example. - [[MATH310F26(Workbook 1 Companion) - The phase line and what f-prime tells you]] — equilibria, linear stability analysis, the phase line, and trajectories, with four-language code - 📄 [[MATH310F26_WB1.pdf|Workbook 1 — Harvesting a fishery at a constant rate (blank, 1 page)]] - [[MATH310F26(Workbook 2 Companion) - Taylor series and the art of cancellation]] — Taylor expansions at $x_0\pm\Delta x$, the odd/even cancellation, and order of accuracy observed, with four-language code - 📄 [[MATH310F26_WB2.pdf|Workbook 2 — The centered difference for $f'$ from Taylor series (blank, 1 page)]] - [[MATH310F26(Workbook 3 and 4 Companion) - One least-squares step, and a discovered equation]] — rates from samples, the normal equations by hand, and the discovered logistic law *(worked page — posts after collection)* - 📄 [[MATH310F26_WB3and4.pdf|Workbooks 3 & 4 — Discovering the logistic equation from three points (blank, 2 pages)]] - [[MATH310F26(Workbook 5 Companion) - Splitting a series by parity]] — absolute convergence as a license to reorder, the parity split worked on $e^\theta=\cosh\theta+\sinh\theta$, the $i^n$ cycle, and partial sums in four languages - 📄 [[MATH310F26_WB5.pdf|Workbook 5 — Prove Euler's formula (blank, 1 page)]] - [[MATH310F26(Workbook 6 Companion) - What a conjugate pair extracts]] — conjugation as reflection, the extraction identities, and the mirrored-pair template taught on $\cosh$/$\sinh$ and a general $c$, $\bar c$ pair - 📄 [[MATH310F26_WB6.pdf|Workbook 6 — Euler's formula, sinusoids, and periodic functions (blank, 1 page)]] - [[MATH310F26(Workbook 7 Companion) - Two tones and a constant, transformed]] — the one-transform-we-own, linearity, and the sifting inverse check, taught on a two-frequency chord (with an FFT animation) and a constant - 📄 [[MATH310F26_WB7.pdf|Workbook 7 — Fourier transformation of sinusoids (blank, 1 page)]] # Previous Semester Landing Pages - [[MATH310 - Spring2026]] - [[MATH310 - Fall 2025]] - [[MATH310 - Spring 2025]] - [[MATH310 - Fall 2024]]