Heart Proofs One proof a day keeps the doctor away

Proofs

Proofs and Exercises

Linear Algebra

HUJI Linear Algebra 1

Determinants and Volume Functions

  1. Semester 2026A, Exam A, Q2

Linear Transformations

  1. Semester 2026A, Exam A, Q6
  2. Semester 2026A, Exam A, Q7

Matrices and Invertibility

  1. Semester 2026A, Exam B, Q1
  2. Semester 2026A, Exam A, Q8

Matrix Representations of Linear Maps and Change of Basis Matrices

  1. Semester 2026A, Exam A, Q1
  2. Semester 2026A, Exam A, Q9

Spans, Bases and Dimensions

  1. Semester 2026A, Exam B, Q3
  2. Semester 2026A, Exam A, Q4
  3. Semester 2025B, Exam B, Q1

Systems of Linear Equations

  1. Semester 2026A, Exam A, Q3

Linear Algebra Done Right by Axler

Chapter 1: Vector Spaces

  1. Result 1.45

Chapter 2: Finite-Dimensional Vector Spaces

  1. Exercises 2B, Q1

Real Analysis

HUJI Infinitesimal Calculus 1

Derivatives

  1. Fermat’s Theorem

Functions

  1. The intermediate value theorem
  2. Weierstrass Extreme Value Theorem
  3. Weierstrass Boundedness Theorem

Quizzes

  1. Semester 2026A, Quiz 4

Sequences

  1. A Problem on the Convergence of a Recursive Sequence Depending on Its Initial Value
  2. The Bolzano-Weierstrass Theorem
  3. Semester 2026A, Exam A, Q1

The Field of Real Numbers

  1. Archimedean Property

HUJI Infinitesimal Calculus 2

Quizzes

  1. Semester 2026B, Quiz 1