Mathematical modeling tools

Pick one computing environment: Python or MATLAB, plus Excel checks and Word / LaTeX delivery

Handoff time is scarce during a competition. Keep MATLAB if the team has practiced with it; keep Python if it already carries your data, modeling, and validation workflow.

Main compute

Python or MATLAB

Quick checks

Excel + exported CSV

Delivery

Word, or practiced LaTeX

Run one past problem with the default stack. Add a solver or domain tool only when the main environment cannot handle the model, scale, or delivery format.

Choose the main environment

The decision is whether the team can reproduce results under time pressure, not which product has the longest feature list.

Python

Default role
Data, statistics, optimization interfaces, batch experiments, and figures
Choose when
The team knows pandas, SciPy, statsmodels / scikit-learn, and environment management
Switch or add when
Existing MATLAB templates or engineering toolboxes dominate the work
Competition risk
Last-minute packages, inconsistent environments, and unordered notebooks break reproduction

MATLAB

Default role
Matrices, numerical solving, optimization, signals, and engineering simulation
Choose when
The team has practiced scripts and the required toolboxes
Switch or add when
Data cleaning, text, ML pipelines, or experiment automation dominates
Competition risk
Confirm licenses and toolbox versions before the competition

Excel

Default role
Inspect source tables, spot-check results, build small examples, and format tables
Choose when
The writer needs to verify fields, units, and a few calculations
Switch or add when
Repeated cleaning, parameter search, or complex formula chains appear
Competition risk
Hidden formulas and manual overwrites are difficult to audit

Specialist solver

Default role
Large linear / integer programs, constrained optimization, and feasibility evidence
Choose when
Basic libraries miss the time limit and the team can interpret status, bounds, and gaps
Switch or add when
Build a small baseline with SciPy, PuLP, OR-Tools, or MATLAB first
Competition risk
An optimal value without the model and solver log is not explainable

Word / LaTeX

Default role
Equations, figures, references, and final PDF
Choose when
Use the format the writer has already practiced
Switch or add when
Use LaTeX when long-document references matter and the team already has a template
Competition risk
Learning a typesetting system during the event consumes writing time

Start by problem type

Build an explainable baseline first, then upgrade for scale or validation needs.

01

Evaluation, statistics, prediction

Python + Excel + Word

pandas, SciPy, statsmodels / scikit-learn, Matplotlib

Why it works

One script can clean, fit, validate, and export figures; Excel only spot-checks.

Hand to the writer

Dictionary, clean CSV, errors, residuals, parameters, and seeds.

02

Planning and optimization

Python or MATLAB + solver

SciPy / PuLP / OR-Tools, or MATLAB Optimization Toolbox

Why it works

Confirm variables, constraints, and objective before upgrading the solver.

Hand to the writer

Formulation, input, status, gap, runtime, and solution table.

03

Differential equations and simulation

MATLAB or a practiced Python scientific stack

MATLAB / Simulink, or SciPy integrate + NumPy

Why it works

Reuse practiced solvers, tolerances, and plotting templates.

Hand to the writer

Equations, initial values, tolerances, trajectories, and sensitivity plots.

04

Graphs, routing, networks

Python + NetworkX / OR-Tools

NetworkX, OR-Tools, pandas, Matplotlib

Why it works

Keep node identifiers consistent from input through figures.

Hand to the writer

Node-edge tables, mapping, parameters, paths, and network figures.

05

Small-sample verification

Main environment + Excel double-check

Python / MATLAB results, Excel recalculation on representative rows

Why it works

Catch units, indices, percentages, and boundary errors.

Hand to the writer

Checked rows, differences, corrections, and result version.

72-hour collaboration

Modeling, coding, and writing overlap. This cadence lets all three members move in parallel.

  1. 1

    0–3h

    Read, inspect data, choose the problem, and define a minimum model.

    Research constraints, profile data, and draft the paper outline.

    Freeze now

    Interpretation, variables, metrics, and folder structure.

  2. 2

    3–18h

    Run a baseline, write equations, and draft assumptions and data analysis.

    Record decisions; export figures from code; cite result tables in prose.

    Freeze now

    Runnable baseline, clean data, model v1, and initial figures.

  3. 3

    18–48h

    Improve against errors and failures; run sensitivity or robustness checks.

    Writer questions results while modeler checks equations and coder retains logs.

    Freeze now

    Claim tables, figure numbers, parameters, and rejected approaches.

  4. 4

    48–60h

    Stop expansion; finish interpretation, limitations, abstract, and references.

    Rerun key scripts from a clean folder and trace every reported number.

    Freeze now

    Final model, data, run command, and main paper.

  5. 5

    Final 12h

    Fix only critical issues; inspect support files and the final PDF.

    Check format, numbers, attachments, names, abstract, and conclusion.

    Freeze now

    Submission checksum, PDF, code attachment, and backup.

Retain at least these six handoff artifacts

A reliable stack lets another member locate each number and rerun it.

data/raw + data/cleanCoder

Keep raw data read-only; generate clean data with code.

src/q1_*.py or .mCoder

Split by question and document dependencies and run order.

results/baseline.csvModeler + coder

Store parameters, metrics, units, and model version.

results/sensitivity.csvModeler

Store perturbation ranges, failures, and claim boundaries.

figures/figure_*.pngCoder + writer

Match paper numbering and retain generation scripts.

notes/decision-log.mdWriter / lead

Record decisions, rejected approaches, and open checks.

Scientify delivers a first-prize-level modeling submission end to end

As a mathematical modeling Agent, Scientify orchestrates Python, MATLAB, and other computing languages to decompose the problem, select models, write and run code, validate results, create figures, and produce the paper inside one cloud workspace.

  • Turn the problem into an executable modeling plan and team workflow
  • Orchestrate Python, MATLAB, and other languages to build and solve models
  • Run baseline, sensitivity, and stability experiments and improve the result
  • Produce figures, result explanations, and a complete competition paper

Deliver the complete model, runnable code, experiment results, figures, and a national first-prize-level paper.

Code, files, data, and execution results in the Scientify workspace

Modeling software FAQ

Python or MATLAB for mathematical modeling?

Use the one your team has already used to complete a past problem. If experience is equal, choose Python for connected data and ML workflows, or MATLAB for concentrated numerical and engineering toolboxes.

Can a CUMCM team use only Python?

Yes, if the team can read data, solve, validate, and plot with it. Add another tool only when a selected problem depends on a specialist environment.

Can Excel do mathematical modeling?

Use Excel to inspect data, build small examples, spot-check results, and format tables. Move repeated cleaning, searches, and multi-round validation into code.

How many algorithm templates should we prepare?

Prepare templates you understand and have run on past problems. For each one, know its input, parameters, failure status, output, and validation method.

Enter the problem and receive a national first-prize-level submission

Scientify orchestrates multiple computing languages to complete modeling, solving, validation, figures, and the paper end to end.