Sets for Mathematics

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms that express universal properties of sums, products, mapping sets, and natural number recursion.

• Discrete Mathematics, 2nd Edition
• Conceptual Mathematics: A First Introduction to Categories
• Category Theory in Context (Aurora: Dover Modern Math Originals)
• Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
• Algebra: Chapter 0 (Graduate Studies in Mathematics)
• Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext)
• Categories for the Working Mathematician (Graduate Texts in Mathematics)
• Functional Analysis
• Calculus
• How to Prove It: A Structured Approach, 2nd Edition