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Overview

Course Prescription

Logic addresses the foundations of mathematical reasoning. It models the process of mathematical proof by providing a setting and the rules of deduction. This course builds a basic understanding of first order predicate logic, introduces model theory and demonstrates how models of a first order system relate to mathematical structures. Recommended for high level computer science or mathematical logic.

Course Overview

The course content is split into two halves. In the first half, we develop sentential logic (also known as statement logic or propositional logic). We develop this from both semantic and syntactic perspectives, that is, from a study of implication, and from a formal study of proofs. We will also consider the relationship between these notions. In the second half, we develop a richer logical system called predicate (or first order) logic, which allows us to formalise many ideas from mathematics. In particular, this is the system in which set theory is typically developed, and in which axioms for many mathematical systems are expressed. In this course, predicate logic is studied from both the syntactic and semantic perspectives, paralleling the ideas developed for sentential logic in the first half of the course.

The course is designed to provide an understanding of many of the mathematical concepts and methods involved in mathematical logic and computer science.

This course could be of interest to students majoring in mathematics and/or computer science. The skills gained in this course may be of particular use to any students interested in formal systems, or in further study of the foundations of mathematics.

Key Topics

  • Informal statement logic: statements and truth tables; logical laws; soundness and adequacy; arguments and validity.
  • Formal statement logic: Post production systems; the system L; the deduction theorem; truth assignments; adequacy.
  • Informal predicate logic: first order logic; interpretations; logical validity, implication, and equivalence; Prenex normal; substitutions.
  • Formal predicate logic: the formal system K_L; the deduction theorem; models and consistency; soundness and adequacy; compactness.
  • First order systems: equality; normal models; Peano postulates; first order arithmetic; working in N.
  • Additional topics applying knowledge from first order logic (if time permits).

Workload Expectations

This course is a standard 15-point course and students are expected to spend 10 hours per week involved in each 15-point course that they are enrolled in. For each week of this course, you can expect 3 hours of lectures, a 1-hour tutorial, 3 hours of reading and thinking about the content and 3 hours of work on assignments and/or test preparation.

Course Prerequisites, Corequisites and Restrictions

Prerequisite

Locations and Semesters Offered

LocationSemester
City

Teaching and Learning

Campus Experience

Lectures will be available as recordings.

  • The activities for the course are scheduled as a standard weekly timetable.

  • Learning Resources

    Taught courses use a learning and collaboration tool called Canvas to provide students with learning materials including reading lists and lecture recordings (where available). Please remember that the recording of any class on a personal device requires the permission of the instructor.

    Additional Information on Learning Resources

    The MATHS 315 course book will be available on canvas, or a hard copy can be purchased from the Students Resource Centre.

    Copyright

    The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.


    You may copy the course content for the purposes of private study or research, but you may not upload onto any third-party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

    Learning Continuity

    In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

    Academic Integrity

    The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

    Similarly, research students must meet the University’s expectations of good research practice. This requires:

    • Honesty - in all aspects of research work
    • Accountability - in the conduct of research
    • Professional courtesy and fairness – in working with others
    • Good stewardship – on behalf of others
    • Transparency – of research process and presentation of results
    • Clarity - communication to be understandable, explainable and accessible

    For more information on the University’s expectations of academic integrity, please see the Academic Conduct section of the University policy hub.

    Disclaimer

    Elements of this outline may be subject to change. The latest information about taught courses is made available to enrolled students in Canvas.

    Students may be asked to submit assessments digitally. The University reserves the right to conduct scheduled tests and examinations online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.


    Assessment and Learning Outcomes

    Course Learning Outcomes

    CLO #OutcomeProgramme Capability Link
    1
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    6
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    8

    Assessments

    Assessment TypeAssessment PercentageAssessment Classification

    Assessment to CLO Mapping

    Assessment Type12345678

    Student Feedback, Support and Charter

    Student Feedback

    Feedback on taught courses is gathered from students at the end of each semester through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions. Your feedback helps teachers to improve the course and its delivery for future students. In addition, class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.

    Additional Information on Student Feedback

    Student feedback on the introduction of a set theory component has been very positive. Efforts will be made to incorporate such a component in the future.

    Class representatives

    Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

    Tuākana

    Tuākana is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at Tuakana Learning Communities.

    Additional Information on Tuākana

    Whanaungatanga and manaakitanga are fundamental principles of Tuākana Maths, a community of learning for Māori and Pasifika students taking mathematics courses. The Tuākana Maths programme provides workshops, drop-in times, and a space where Māori and Pasifika students can work alongside our Tuākana tutors and other Māori and Pasifika mathematics students.

    Inclusive Learning

    All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

    Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website.

    Wellbeing

    We all go through tough times during the semester, or see our friends struggling. There is lots of help out there - please see the Support Services page for information on support services in the University and the wider community.

    Special Circumstances

    If your ability to complete assessed work is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due. If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page. This should be done as soon as possible and no later than seven days after the affected test or exam date.

    Student Charter and Responsibilities

    The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter.

    Student Academic Complaints and Disputes

    Students with concerns about teaching including how a course is delivered, the resources provided, or supervision arrangements, have the right to express their concerns and seek resolution. The university encourages informal resolution where possible, as this is quicker and less stressful. For information on the informal and formal complaints processes, please refer to the Student Academic Complaints Statute in the Student Policies and Guidelines section of the Policy Hub.