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Mathematics & Engineering
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Number Theory

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Number Theory. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Divisibility; Euclidean algorithm; Primes; Unique factorization. Congruences; Chinese remainder theorem; Modular inverses; Orders. Quadratic residues; Legendre symbols; Quadratic reciprocity; Residue computation. Arithmetic functions; Dirichlet convolution; Mobius inversion; Multiplicative sums. Diophantine equations; Pell equations; Descent; Rational points. Continued fractions; Diophantine approximation; Convergents; Irrationality. Algebraic integers; Norms; Ideals; Failure of factorization. Prime distribution; Zeta function; Computational experiments; Number-theoretic proofs. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.

32h Certificate available
InternationalAcademic (University)Independent preparation

Curriculum

One complete track with its own final exam and certificate.

Independent university-level study of Number Theory. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Divisibility; Euclidean algorithm; Primes; Unique factorization. Congruences; Chinese remainder theorem; Modular inverses; Orders. Quadratic residues; Legendre symbols; Quadratic reciprocity; Residue computation. Arithmetic functions; Dirichlet convolution; Mobius inversion; Multiplicative sums. Diophantine equations; Pell equations; Descent; Rational points. Continued fractions; Diophantine approximation; Convergents; Irrationality. Algebraic integers; Norms; Ideals; Failure of factorization. Prime distribution; Zeta function; Computational experiments; Number-theoretic proofs. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.

Divisibility; Euclidean algorithm; Primes; Unique factorization

  • Divisibility, the Division Algorithm, and Ideal Lattices in Z Lab60 min
  • The Euclidean Algorithm, Complexity, and Lamé's Bound Lab60 min
  • Prime Numbers, Euclid's Lemma, and Infinitude Proofs Lab60 min
  • The Fundamental Theorem of Arithmetic and Factorization Lattices Lab60 min

Careers this prepares you for

    How you study

    Every lesson pairs an in-depth video with written notes, key takeaways, a hands-on lab, exercises and a quiz. Work at your own pace, then sit the final examination for your Erudex certificate.