design a syllabus to teach me linear algebra
Structured AI conversations for learning and research
Turn long, linear AI chats into navigable conversation trees.
Email: support@colcoor.com
Works in VS Code and Cursor with Anthropic, Gemini and Cursor CLI. More providers are coming. Run locally with no backend, or connect for collaboration.
- Module 0: Mathematical foundations
- Module 1: Systems of linear equations and matrices
- Module 2: Vector spaces
- Module 3: Linear transformations
Let's start with Module 0
Since a proof-based linear algebra course relies heavily on clear logical thinking and precise language, starting with Module 0 will give you the vocabulary you need.
Module 0 completed, Let's continue with Module 1
Modules 0 and 1 completed, Let's continue with Module 2
Modules 0-2 completed, Let's continue with Module 3
Learning comparison
Same course. Two conversation structures.
Over 90% fewer input tokenswith stronger syllabus adherence in the tree-structured conversation
This recorded proof-based linear algebra course used the same model, syllabus, seed, and temperature=0 in both runs. The difference was how the conversation context was structured.
Linear chat
4,250,811 input tokensEvery completed lesson, clarification, and detour remained in the history sent to later turns, so the context kept growing throughout the course.
Colcoor tree
424,816 input tokensEach branch carried only the context along its active path, so unrelated explorations did not accumulate in later turns or distract the model from the current lesson.
Token totals are provider-reported input context, including cached input. Read the full comparison on GitHub.
The problem
Linear chats break when the work branches
Long AI conversations work well until learning or research splits into questions, alternatives, and side explorations. Then the transcript becomes a growing mix of relevant context, finished detours, old assumptions, and knowledge that is increasingly difficult to revisit.
The chat keeps everything
Clarifications, completed exercises, abandoned hypotheses, and old turns remain in the conversation long after they stop being relevant to the current task.
Exploring creates permanent context
A useful side question may only matter for a few turns, but in a linear chat it becomes part of every turn that follows.
Returning means reconstructing
Revisiting an earlier concept, assumption, or research direction usually means searching through the transcript, starting another chat, or manually rebuilding the context.
The product
A conversation tree for learning and research
Colcoor makes the structure of a long AI conversation explicit. Each branch can hold a lesson, clarification, hypothesis, sub-question, alternative approach, or evidence trail.
When you continue from a point in the tree, the model receives only the conversation path that leads there — while the rest of the exploration remains available to you.
Focused Context
Continue with the context relevant to the current path instead of carrying the entire conversation forward.
Branch Anywhere
Ask a clarification, explore an alternative, or investigate a side question directly from the point where it becomes relevant.
Resume Anywhere
Return to any earlier point and continue from the exact conversation state that existed there.
Organize What Matters
Use notes, highlights, Lists, search, and stars to preserve useful findings across a growing conversation tree.
Use cases
Built for work that branches
Colcoor is most useful when a conversation needs to remain coherent while the work itself moves in multiple directions.
Structured learning
Follow a learning plan while branching into clarifications, exercises, examples, and deeper questions — then return to the main path without carrying every detour forward.
Research
Explore competing hypotheses, interpretations, and lines of evidence while preserving the context behind each direction.
Literature and evidence review
Investigate individual sources or claims in separate branches, then collect the findings that matter without mixing every exploration into one transcript.
Technical investigation
Compare architectures, designs, assumptions, and alternative approaches while keeping each line of reasoning independently revisitable.
Long-running projects
Return to earlier decisions and continue from the context that existed when they were made instead of reconstructing the discussion later.
Collaborative exploration
Let multiple people investigate different parts of the same conversation tree without forcing every discussion into the same reasoning path.
Workflows
Build structured knowledge from the conversation
The tree keeps different lines of thought separate. Colcoor also provides tools for preserving and connecting what matters across those branches.
Notes and checkpoints
Attach persistent context, decisions, or reminders to the points where they belong, and mark important milestones in a longer process.
Highlights and Lists
Select useful text from across the conversation and collect it into structured Lists with links back to the original messages.
Work from collected findings
Use agents to build Lists from a conversation or perform follow-up work on material you have already collected.
Search and retrieval
Find important messages, notes, starred responses, and previous findings without manually navigating the entire tree.
Collaboration without context pollution
In connected mode, teammates can share the same conversation tree and use side chat to coordinate without inserting that discussion into the model's active reasoning path.
How it runs
Local for individual work. Connected for collaboration.
The same extension supports both modes. Your conversation structure and model context behave the same way; the difference is where Colcoor stores and shares the conversation.
Local mode
Keep Colcoor conversation data inside the current workspace with no Colcoor backend or account required. Local mode is single-user and does not include shared conversations, side chat, or cross-workspace access.
Connected mode
Use the Colcoor backend when you want shared conversations, collaboration, side chat, and access to the same conversation across workspaces.
Use the model provider you choose
Colcoor currently supports Anthropic directly, Gemini, and Cursor CLI. The model remains separate from the conversation structure: Colcoor determines the explicit context path and sends it to the selected provider.
DownloadBeta
Try Colcoor
Download the Colcoor extension for your platform and install it in VS Code or Cursor. Colcoor is currently in beta and distributed through GitHub Releases.
Windows
Windows x64
Download VSIXmacOS
Apple Silicon (M1, M2, M3, M4)
Download for Apple SiliconLinux
ARM64
Download Linux ARM64Get started
Start using Colcoor
Download the beta extension for VS Code or Cursor and follow the Quick Start Guide. The source code is also available publicly on GitHub.
Colcoor is source-available under the Business Source License 1.1.
FAQ
Questions worth answering early
Why does Colcoor use a conversation tree?
Because long learning and research conversations rarely stay linear. A tree lets you explore a question or alternative from the point where it becomes relevant, then return to the original path without carrying that exploration into every future model call.
Does the model see the entire tree?
No. The model receives the selected root-to-node conversation path and the notes that belong to that context. Other branches remain available to you but are not automatically included in the model context.
Why not just use a larger context window?
A larger context window allows the model to receive more history, but it does not make all of that history relevant. Colcoor is designed to keep the active context aligned with the current line of work rather than repeatedly sending unrelated branches simply because they fit.
Is Colcoor only for coding?
No. Colcoor runs in VS Code and Cursor today, but it is designed primarily for learning, research, and other long-running knowledge work. The editor is the current interface, not the intended limit of the product.
Can I use Colcoor without a backend?
Yes. In local mode, Colcoor stores the conversation in the workspace and requires no Colcoor backend or sign-in. Model requests still use whichever model provider you select.
Which model providers are supported?
Colcoor currently supports Anthropic directly, Gemini, and Cursor CLI. Additional providers can be added without changing the conversation-tree model.
What changes in connected mode?
Connected mode adds shared conversations, collaboration, side chat, and access beyond a single local workspace. The underlying conversation-tree and context-selection model remains the same.
Is Colcoor available now?
Yes. Colcoor is currently available as a beta release for VS Code and Cursor. Download the VSIX for your platform above and follow the Quick Start Guide.
Which file should I download?
Choose Windows x64 for most Windows PCs, Apple Silicon for M-series Macs, Intel Mac for older Intel-based Macs, and the matching x64 or ARM64 build for Linux.