Hawaii Pacific University
MATH 1110 Introduction to Mathematical Logic Section ____
Semester and year, meeting times
Instructor: Name, contact information and other relevant information about the instructor.
Course description: An introduction to mathematical logic covering Sentential and First Order Logic
including the methodology of writing mathematical proofs; the course will look at logic from both the
syntactic and semantic perspective. Topics include the deductive calculus, valid forms, the Soundness
Theorem, and some programming in a functional language such as Scheme.
Course prerequisite: MATH 1105
General Education Requirement: This course is classified under the Research and Epistemology Theme
and meets the requirement for a course in Research & Epistemology B: Numeracy and Quantitative
Reasoning.
General Education Student Learning Outcomes and the Five Themes: HPU’s general education
curriculum is focused around five themes. This course emphasizes the Research and Epistemology
Theme and provides students with opportunities to achieve the following related general education
student learning outcomes.

Students will seek and achieve understanding of numerical data. In addition to recursive code,
students will work with truth tables , Venn Diagrams and Boolean Algebras to help achieve
understanding of numeric and symbolic data. Students will have to work with both the English
and symbolic representations of statements, and understand the truth values for each form.

Students will recognize the multiple interpretations numerical data permit and ways
that they can be manipulated. Students study mathematical sequences and learn how
recursive code generates interesting sequences. Student activities lead them to analyze these
sequences for patterns and write them as symbolic rules. Students will understand the
semantics of formal theories and how it relates to data

Students will identify a research question or problem, gather and organize relevant
information, apply problem solving strategies, and communicate the results to
others. Students complete both a Scheme project and writing assignment involving a
mathematical or logical proof and its conveyance. The writing assignment will involve a
synthesis of the proof strategies covered in the class. The Scheme project will test their
knowledge of how to solve a mathematical problem through recursion, and the Scheme
methods of abstraction and application.

Students will utilize methods and technologies appropriate to the discipline to
investigate research questions, generate predictions, test hypotheses and/or solve
problems. Students will learn several ways of investigating validity of formulas in first order
logic and will utilize such methods throughout the class. Students will utilize Scheme to solve
mathematical problems and investigate the difference between primitive recursion and
recursion through the technological medium.
Note: Purple text shows places where specific course information must be filled in. Red text contains
explanatory notes to the instructor which should be deleted before using the syllabus. Blue explanations
above should be rephrased by the individual instructor to reflect the specific approach in that section of
the course. Course specific outcomes below are an example and may also be rephrased or modified by
the instructor.
Student Learning Outcomes for MATH 1115 Survey of Mathematics
Upon the successful completion of this course, students should be able to:
 Demonstrate understanding of the relationship between tautological implication and
deducibility as measured through homework assignments
 Follow the style of writing a proof in mathematics as measured by written assignments
 Find an equivalent disjunctive normal form for a sentence of sentential logic as measured by
quizzes and homework
 Accurately figure out a truth table for a sentence of sentential logic
 Translate English sentences into sentences of First Order Logic as measured by quizzes and
homework
 Negate a Quantified Formula as measured by quizzes and homework
 Demonstrate an understanding of the meaning of the universal and existential quantifiers as
measured by exams
 Employ Modus Ponens in proofs as measured by quizzes and homework
 Understand Satisfiability of a Theory in a Model
 Utilize and master Fundamental Proof Techniques as measured by quizzes and homework and in
class presentations
 Grasp the relationship between syntax and semantics in logic
 Perform some basic programming in Scheme as measured by lab exercises and programming
assignments
For the rest of these required syllabus items see the details in the faculty handbook. Delete this note
once the syllabus is complete. For online courses there are some additional requirements given at this
link.
Texts List textbooks with ISBN’s and include this language as well
All textbook information (pricing, ISBN #, and e-books) for this course can be found on the HPU
Bookstore website: hpu.edu/bookstore.
If you have any questions regarding textbooks, please contact the HPU Bookstore at:
Phone:
808-544-9347
Or e-mail:
jyokota@hpu.edu
mmiyahira@hpu.edu
Assignments and mode of evaluation
Summary of important dates and deadlines (if the schedule is a separate document and due dates are
not given with the description of the assignments).
Class rules and policies (including regarding attendance, late work and academic dishonesty)
Schedule of events (may be attached separately)