Mathematical Logic: A Course With Exercises – Propositional Calculus, Boolean Algebras, Predicate Calculus by Rene Cori

Introduction

Mathematical logic is the bedrock of all precise reasoning, and for Indian students pursuing advanced studies in mathematics, computer science, or philosophy, a firm grasp of its principles is indispensable. Mathematical Logic: A Course With Exercises—Propositional Calculus, Boolean Algebras, Predicate Calculus by René Cori is a rigorous yet accessible textbook that guides learners through the foundational layers of logic. Published by Oxford University Press, this hardcover volume is designed for undergraduate and postgraduate students who wish to build a solid theoretical foundation while engaging with practical problem-solving.

Book Overview

This book adopts a model-centric approach to logic, making abstract concepts tangible through clear exposition and structured exercises. The journey begins with propositional calculus, moves through Boolean algebras, and culminates in predicate calculus and completeness theorems. Every chapter is complemented by a rich set of exercises, with full solutions provided at the end—making it an ideal self-study companion for Indian classrooms and competitive examinations alike.

Key Highlights

• Comprehensive coverage of propositional calculus, Boolean algebras, and predicate calculus in one cohesive volume.
• Over 200 graded exercises with complete answers, enabling progressive learning and self-assessment.
• Model-based pedagogy that clarifies how logical systems relate to mathematical structures.
• Rigorous yet readable—suitable for advanced undergraduates and beginning postgraduates.
• Hardcover edition from OUP Oxford, built to withstand years of reference and study.

Inside the Book

The text is divided into three major parts. Part I explores propositional calculus, introducing syntax, semantics, truth tables, and natural deduction. Part II delves into Boolean algebras, linking logical operations to algebraic structures. Part III covers predicate calculus, including quantifiers, first-order logic, and the celebrated completeness theorems. Each section builds logically on the previous, and the exercises are carefully sequenced to reinforce understanding before moving forward.

Key Topics

• Propositional connectives and truth-functional semantics
• Natural deduction and proof strategies
• Boolean algebras: axioms, homomorphisms, and representations
• First-order predicate logic: syntax, semantics, and models
• Completeness and compactness theorems
• Applications of logic in mathematics and computer science

Reader Benefits

Indian students often face a gap between intuitive understanding and formal reasoning. This book bridges that gap by offering clear explanations alongside abundant practice. The inclusion of complete solutions means learners can verify their work independently, making it perfect for self-study during semester breaks or exam preparation. The logical progression also helps teachers design course modules with confidence.

Learning Outcomes

• Master the syntax and semantics of propositional and predicate calculi.
• Understand the algebraic underpinnings of logic through Boolean algebras.
• Prove completeness theorems and appreciate their significance.
• Develop rigorous proof-writing skills applicable across mathematics.
• Prepare for advanced topics in model theory, set theory, and computability.

Who Should Read

This book is ideal for advanced undergraduate students in mathematics, computer science, and philosophy. It is also highly recommended for postgraduate students needing a refresher in foundational logic, as well as for self-taught enthusiasts who want a structured, exercise-driven approach. Teachers and researchers in logic will find it a valuable reference for course design and problem selection.

About the Author

René Cori is a distinguished French mathematician and logician, known for his contributions to mathematical logic and model theory. He has taught at the University of Paris and has authored several influential textbooks. His writing style combines precision with pedagogical clarity, making complex topics accessible to serious students. Cori’s long experience in teaching logic shines through in the thoughtful arrangement of material and exercises.

About the Publisher

Oxford University Press (OUP) is a globally respected academic publisher with a long tradition of producing high-quality textbooks in mathematics and the sciences. OUP’s commitment to rigorous editing, durable binding, and accurate typesetting ensures that every copy meets the standards expected by students and educators. This hardcover edition is built to last, making it a worthy addition to any serious library.

Conclusion

Mathematical Logic: A Course With Exercises is more than a textbook—it is a complete learning system. With its blend of theory, practice, and complete solutions, it empowers Indian students to master logic at their own pace. Whether you are preparing for university exams, competitive tests like the GATE or NET, or simply seeking to sharpen your analytical skills, this book will serve as a trusted guide. Order your copy today from Bookshops.in and take a decisive step toward logical mastery.