In this short “exploration” chapter we consider an alternative semantics for modal logic using topological spaces. No background whatsoever in topology is assumed. We motivate the fundamental mathematical definition of a topological space from an epistemic perspective, and connect it to the modal logics studied previously, both intuitively and formally. We also show how to transform reflexive and transitive frames into topological spaces in a truth-preserving way, and use this to establish completeness.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.

Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.

The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.

Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.

• 300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.

• Provides a one-stop resource for both classical and modern coding techniques.

• Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.

• 180 worked examples guide students through the practical application of the theory.

Channel coding lies at the heart of digital communication and data storage. Fully updated to include current innovations in the field, including a new chapter on polar codes, this detailed introduction describes the core theory of channel coding, decoding algorithms, implementation details, and performance analyses. This edition includes over 50 new end-of-chapter problems to challenge students and numerous new figures and examples throughout.

The authors emphasize a practical approach and clearly present information on modern channel codes, including polar, turbo, and low-density parity-check (LDPC) codes, as well as detailed coverage of BCH codes, Reed–Solomon codes, convolutional codes, finite geometry codes, and product codes for error correction, providing a one-stop resource for both classical and modern coding techniques.

Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then begin with classical codes, continue with modern codes, and extend to advanced topics such as code ensemble performance analyses and algebraic LDPC code design.

• 300 varied and stimulating end-of-chapter problems test and enhance learning, making this an essential resource for students and practitioners alike.

• Provides a one-stop resource for both classical and modern coding techniques.

• Starts with the basic theory before moving on to advanced topics, making it perfect for newcomers to the field of channel coding.

• 180 worked examples guide students through the practical application of the theory.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.

Explore the fundamentals of biomedical engineering technologies with this thought-provoking introduction, framed around modern-day global cancer inequities. Connecting engineering principles to real-world global health scenarios, this textbook introduces major technological advances in cancer care through the lens of global health inequity, discusses how promising new technologies can address this inequity, and demonstrates how novel medical technologies are adopted for real-world clinical use. It includes modular chapters designed to enable a flexible pathway through the material for students from a wide range of backgrounds; boxed discussion of contemporary issues in engineering for global health, encouraging students to explore ethical questions related to science and society; supplementary lab modules for hands-on experience in translating engineering principles into healthcare solutions; and over 200 end-of-chapter problems targeting multiple learning outcomes to solidify student understanding. Designed to equip students with all the critical, technical, and ethical knowledge they need to excel, this is the ideal introduction for students in biomedical engineering and global health.