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Community

A place for careful mathematics.

Ask precise questions, work through curated problems, read technical material together, and share what you notice in the Math Lab. Every post and reply is reviewed by a moderator before it is published.

Browse channelsHow to join
Channels
8 topic channels
Curated prompts
19 problems and reading questions
Moderation
Every contribution reviewed before publication
Membership
Free; sign in and choose a display name

Topic channels

Eight channels, each with curated prompts.

From the problem desk

Start with a curated prompt.

  • Calculus & Analysis

    Differentiating under the integral sign

    Let I(s)=∫01cos⁡(ts) dtI(s) = \int_0^1 \cos(ts)\,dt. Compute I(s)I(s) directly, then compute I′′(s)I''(s) in two ways: by differentiating your closed form, and by differentiating under the integral sign. Which conditions justify the second method?

    Discuss

  • Transforms & Operators

    Where does a Laplace transform live?

    For f(t)=e2tsin⁡tf(t) = e^{2t}\sin t, find L{f}(s)\mathcal{L}\{f\}(s) and its region of convergence. Why is the formula meaningful outside that region only through analytic continuation?

    Discuss

  • Linear Algebra & Matrices

    The matrix of d/dxd/dx

    Write the matrix of differentiation on the space spanned by {1,x,x2,x3}\{1, x, x^2, x^3\}. Why is it nilpotent? What is its matrix on {sin⁡x,cos⁡x}\{\sin x, \cos x\}, and what are its eigenvalues?

    Discuss

Member discussions

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Study together

Study circles and sessions.

Small groups formed on request around a pathway or a book chapter, and live sessions scheduled when there is a group to meet.

Study circles

  • Calculus Foundations Circle
  • Transform Methods Circle
  • Book Reading Circle
  • Linear Algebra & Matrix Methods Circle
Study circles

Session formats

  • Reading session
  • Lab walkthrough
  • Problem clinic
  • Lecture for a group or institution
Sessions and events

Guidelines

How the community works.

  • Be precise and generous

    Explain your reasoning, define your notation, and assume good faith in others.

  • Show your attempt

    Questions should include what you tried and where it stops. Posts that only ask for answers are declined.

  • Respect academic integrity

    Do not post current graded assignments, quizzes, or exam questions, and do not complete them for others.

  • Separate claims from conjectures

    Say whether something is a classical result, a result from a source, or your own idea. Cite sources.

  • Keep it mathematical

    No advertising, solicitation, or off-topic material. No personal information about yourself or others.

  • Disagree with arguments, not people

    Point to the step you doubt. Harassment or dismissive language leads to removal.

Full guidelines, moderation, and integrity policy