Pure and Applied Logic

The Bachelor of Science in Pure and Applied Logic at Carnegie Mellon University offers students a comprehensive foundation in the fundamental principles of logical reasoning, formal systems, and their applications across various disciplines. This interdisciplinary program combines rigorous theoretical coursework with practical applications, preparing students for careers in academia, research, artificial intelligence, computer science, philosophy, and cognitive science. Throughout the program, students explore topics such as propositional and predicate logic, model theory, proof theory, computational logic, and the philosophical underpinnings of logic. They also gain skills in mathematical reasoning, formal language analysis, and the development of logical frameworks used in computer programming and software development. The curriculum emphasizes the importance of clarity, precision, and analytical thinking, providing students with tools to approach complex problems systematically. In addition to core courses, students have opportunities to engage in advanced seminars, research projects, and collaborative learning environments that foster critical thinking and innovation. The program encourages the integration of logic with other areas such as mathematics, computer science, and philosophy, enabling students to understand and contribute to cutting-edge developments in these fields. With access to world-class faculty and state-of-the-art resources, students are well-prepared to pursue graduate studies or enter the workforce in roles that require logical analysis, algorithm design, and theoretical research. Graduates of the Pure and Applied Logic program are equipped to make significant contributions to technology, science, and philosophical inquiry, reflecting Carnegie Mellon University’s commitment to interdisciplinary excellence and intellectual rigor.

The program's flexible requirements provide a broad curricular grounding, steady involvement in research, and the opportunity to practice the craft of teaching in an excellent undergraduate environment. Students are expected to complete a thesis by the middle of their third year, and a PhD thesis by the end of their fifth year.

Coursework

The program's course requirements are designed to provide students with a shared introduction to basic tools of philosophical analysis, a shared background of philosophical issues, significant interdisciplinary competence and an introduction to research topics in the department.

Core Philosophy requirements (4 courses)

• 80-600 Philosophy Core Seminar: Survey of crucial research in philosophy, logic, and related areas
• 80-601 Philosophy Core Seminar II: Continued survey of crucial research in philosophy, logic, and related areas
• 80-616 Formal Methods (1.5 semester): An introduction to contemporary formal frameworks, including Bayes Nets, Decision Theory, Game Theory, and Formal Learning Theory
• 80-618 Topics in Logic II (half semester): The theory of computability, and Gödel's incompleteness theorems
• Professional development seminar: Students must enroll in the professional development seminar in the spring semester of each of their first three years

Mathematics requirements (8 courses, sufficient to earn an MS in Mathematical Sciences)

• One course in algebra (such as 21-610 Algebra I, 21-611 Topics in Algebra, or 80-713 Category Theory)
• One course in topology (such as 21-651 General Topology)
• One course in analysis (such as 21-720 Measure and Integration or 21-721 Probability)
• Three courses in logic (such as 21-602 Set Theory, 21-603 Model Theory, 21-604 Recursion Theory, or 80-711 Proof Theory)
• Two electives in mathematics or computer science

At most two of the eight courses can be taken outside of Mathematics. Students should contact the Director of Graduate Studies of the Mathematics Department to determine if courses taught outside of Mathematics will satisfy this requirement.

Breadth (2 courses)

• One course in the analytic tradition (such as 80-605 Rational Choice, 80-612 Philosophy of Mathematics, or  80-680 Philosophy of Language)
• One course in the history of philosophy (such as 80-254 Analytic Philosophy, or 80-255 Pragmatism)

Electives (4 courses)

• Four unconstrained electives (including directed reading and dissertation research)

These requirements can be filled in three years by taking three courses each semester. Coursework must be completed by the end of the fourth year, at the latest. Electives should be chosen in consultation with the Director of Graduate Studies and the student's advisor, to ensure that the courses chosen will support the student's career goals.

Research

Students are advised to do supervised reading and research with a member of the faculty in the spring of their first year, to explore possible research topics for the MS thesis. In the spring of the second year. The MS thesis itself should be completed by the end of the second year.

In the third year, students choose a dissertation topic and committee. Students must present and defend a prospectus by the end of the fourth year, at the latest, and are expected to complete their doctoral dissertation by the end of the fifth year.

• Graduate application
• Sample of original written work
• Personal research statement
• Three (or more) letters of recommendation
• Transcripts from all previously attended colleges or universities
• GRE scores (Institution code: 2074; Department code: 2801)
• TOEFL or IELTS scores for non-native English speaking applicants
• $50 application fee

Scanned versions of official transcripts, GRE score reports, and TOEFL / IELTS scores can be uploaded in lieu of sending paper copies.

The Bachelor of Science in Pure and Applied Logic at Carnegie Mellon University offers a range of financing options to support students throughout their academic journey. The university provides comprehensive financial aid programs, including need-based grants, scholarships, and work-study opportunities to ensure that qualified students can pursue their education regardless of financial background. Merit-based scholarships are awarded based on academic achievement, leadership qualities, and extracurricular involvement, with some funds designated specifically for students demonstrating exceptional promise in logical reasoning and analytical skills. Federal and state financial aid programs, such as Pell Grants and state-sponsored scholarships, are also available to eligible students, helping to reduce the overall cost of attendance. Additionally, Carnegie Mellon offers graduate assistantships for students enrolled at the graduate level, which provide a stipend and tuition remission in exchange for research or teaching duties. The university encourages students to apply for external scholarships and fellowships from various foundations and organizations supporting science and technology education. Payment plans may be arranged to spread out tuition payments over the academic year, making financial management more manageable. Financial aid applications are handled through the university’s Office of Financial Aid, which provides personalized counseling to help students understand all available resources and plan their finances accordingly. Students are also advised to explore employer tuition reimbursement programs and private loan options, if necessary. Carnegie Mellon’s commitment to affordability and accessibility ensures that students interested in Pure and Applied Logic have access to the necessary financial support to complete their degree successfully.

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Pure and Applied Logic at Carnegie Mellon University offers students an in-depth and rigorous exploration of the fundamental principles and methods underlying logic, computation, and mathematical reasoning. This program is designed for students interested in the theoretical foundations of computer science, mathematics, philosophy, and related disciplines. It emphasizes formal logic, proof theory, model theory, and computability, providing a comprehensive understanding of how logical systems underpin modern computational tools and philosophical inquiries.

The curriculum typically includes courses in propositional and predicate logic, set theory, computational complexity, automata theory, and formal languages. Students engage with both the theoretical and practical aspects of logic, developing skills in formal reasoning, proof construction, and the analysis of logical systems. The program encourages interdisciplinary approaches, connecting logic to fields such as linguistics, artificial intelligence, and cognitive science.

Students have access to state-of-the-art research facilities and benefit from the expertise of faculty members who are leaders in their fields. The program also promotes collaborative research projects, seminars, and workshops that allow students to engage deeply with current topics and innovations in logic and computation. Graduates of the program are well-prepared for careers in academia, research institutions, and industry roles that require strong analytical and logical skills. Additionally, the program serves as a strong foundation for those considering graduate studies in logic, computer science, philosophy, and related disciplines.

Carnegie Mellon University's unique interdisciplinary environment and strong emphasis on computational methodologies provide students with a well-rounded education that prepares them for the complex challenges of the modern technological landscape. The curriculum is periodically updated to reflect the latest developments in research and industry needs, ensuring that students receive relevant and practical knowledge. Through their studies, students acquire critical thinking skills, rigorous analytical abilities, and a deep understanding of the logical principles that form the backbone of computational sciences and philosophical reasoning. This program exemplifies Carnegie Mellon’s commitment to fostering innovation at the intersection of logic, mathematics, and computer science, cultivating future leaders capable of advancing the frontiers of knowledge in these interconnected fields.