Foundations of Mathematical Proof

Path Steps

10 steps · 3 stages. Click any step to inspect it and see it on the Path Map.

Stage 1

Foundation

4 steps

Stage 2

Core Concepts

3 steps

Stage 3

Advanced Topics

3 steps

Resources (0)

Curated materials referenced by this learning path.

No resources for this path yet.

Related Paths

Other paths to continue with, grouped by the theme or type they share with this one.

More Learning Paths

Optogenetics Fundamentals: From Microbial Opsins to In Vivo Neural Control
A structured path for learners who want to understand and apply optogenetics in living animals. It begins with the neurophysiology and photobiology that make light-driven control possible, builds through the molecular biology of channelrhodopsin and halorhodopsin, covers opsin selection, gene delivery, and hardware, and culminates in designing, executing, and interpreting an in vivo optogenetics experiment with appropriate controls. Emphasis is placed on why each opsin behaves the way it does, how to choose among available tools, and how to avoid the common artifacts of light delivery, heating, and expression variability. Learners finish able to read primary optogenetics literature critically and to plan a defensible in vivo manipulation experiment.
IceCube Neutrino Astronomy Basics
A structured introduction to neutrino astronomy through the IceCube Neutrino Observatory. Learners build the physics foundation needed to understand cosmic neutrinos, then progress through Cherenkov detection, the observatory's detector geometry and data acquisition, event signatures, background rejection, and landmark results such as high-energy astrophysical neutrino discovery and multimessenger astronomy. The path ends with the ability to interpret IceCube skymaps, spectra, and alerts at a basic level.
Residential Electrician Training: From Electrical Fundamentals to Service Panel Wiring
This learning path prepares a beginner to perform safe, code-compliant residential electrical work, from understanding electrical theory and reading the National Electrical Code to installing circuits, devices, and a service panel. Learners progress through electrical safety, conductors and raceways, box fill, grounding, overcurrent protection, branch circuits, GFCI/AFCI, and panel wiring, culminating in the ability to plan, install, and troubleshoot a complete residential electrical system. The path emphasizes hands-on practice, code references, and safe work habits expected in an apprenticeship or pre-apprenticeship training program.
Deep Learning and Neural Networks: From Perceptrons to Transformers
A structured, hands-on path from the mathematical foundations of neural computation to building, training, and evaluating modern deep learning models. Learners begin with the perceptron and the backpropagation algorithm, implement networks from scratch, then move to convolutional and recurrent architectures, regularization and optimization techniques, attention and transformer models, and finally transfer learning and deployment. Each node is a self-contained, teachable unit with practical implementation work in Python and PyTorch. Prerequisites are ordered by dependency so that no concept is used before it is introduced.
Rust Programming from Scratch: From First Syntax to Safe Concurrent Systems
A beginner-to-intermediate learning path for the Rust programming language. It starts with toolchain setup and core syntax, then builds a mental model of ownership, borrowing, and lifetimes, and applies it to structs, enums, traits, generics, and error handling. The path continues with collections, smart pointers, concurrency, testing, and Cargo project organization, ending with a capstone command-line application. Each node is a single teachable unit and is ordered so that no step requires knowledge that has not already been introduced.
Rust Programming from Scratch: A Complete Beginner Path
A dependency-ordered path that takes a complete beginner to writing idiomatic, safe, and concurrent Rust programs. It starts with tooling and basic syntax, builds through ownership and borrowing, covers abstraction with structs, enums, traits, and generics, then moves into error handling, collections, testing, and concurrency. The path ends with a capstone project that integrates the language features into a working command-line application. Each node is a single teachable unit and prerequisites are ordered so that no concept is introduced before the knowledge it depends on.

Path Map

Path Steps

Foundation

Core Concepts

Advanced Topics

Resources (0)

Related Paths

More Learning Paths

Optogenetics Fundamentals: From Microbial Opsins to In Vivo Neural Control

IceCube Neutrino Astronomy Basics

Residential Electrician Training: From Electrical Fundamentals to Service Panel Wiring

Deep Learning and Neural Networks: From Perceptrons to Transformers

Rust Programming from Scratch: From First Syntax to Safe Concurrent Systems

Rust Programming from Scratch: A Complete Beginner Path