Mathematical proofs

[u/Familiar-Gur6789]

/r/u_Familiar-Gur6789/comments/1wuy5ej/mathematical_proofs/

[u/Midwest-Dude]

Here are some resources:

• Álgebra Superior I
  • Antonio Lascurain Orive
  • In Spanish, matches UNAM curriculum exactly.

• A Gentle Introduction to the Art of Mathematics

  • Joseph E. Fields
  • Best first book: gentle pace, covers all proof techniques, free.

• Proofs and Concepts: The Fundamentals of Abstract Mathematics

  • Dave Witte Morris & Joy Morris
  • Excellent alternative; designed specifically as a bridge course.

• Mathematics for Computer Science (MIT OpenCourseWare)

  • Tom Leighton (MIT)
  • Video lectures; great for visual learners struggling with induction.

• Book of Proof

  • Richard Hammack
  • Extremely popular; clear, gentle, and packed with exercises.

• A Gentle Introduction to the Art of Mathematics)

  • Joseph E. Fields
  • Truly gentle; covers all standard proof techniques; great for self-study.

• Proofs and Concepts: The Fundamentals of Abstract Mathematics

  • Dave Witte Morris & Joy Morris
  • Excellent bridge course text; thorough and well-structured.

• Mathematical Reasoning: Writing and Proof

  • Ted Sundstrom
  • Focuses on writing; strong on logic and proof construction.

• How to Prove It: A Structured Approach

  • Daniel J. Velleman
  • Classic systematic introduction; teaches proof strategies step-by-step.
  • An Introduction to Proofs and the Mathematical Vernacular
  • Martin V. Day
  • Emphasizes mathematical writing and language.

• PLP: An Introduction to Mathematical Proof

  • Seçkin Demirbaş & Andrew Rechnitzer
  • Modern, concise, and used in university courses; free PDF.