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JOHN CABOT UNIVERSITY
COURSE CODE: "MA 200-1"
COURSE NAME: "Introduction to Mathematical Reasoning"
SEMESTER & YEAR:
Fall 2024
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SYLLABUS
INSTRUCTOR:
Sara Munday
EMAIL: [email protected]
HOURS:
MW 3:00 PM 4:15 PM
TOTAL NO. OF CONTACT HOURS:
45
CREDITS:
3
PREREQUISITES:
Prerequisites: Placement into MA 197 or completion of MA 100 or MA 101 with a grade of C- or above
OFFICE HOURS:
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COURSE DESCRIPTION:
The course introduces the basics of mathematical reasoning, the aspect of mathematics that is concerned with the development and analysis of logically sound and rigorous arguments, which lie at the core of problem-solving and theorem-proving techniques. The course will explore fundamental mathematical concepts such as sets, relations, and functions, and proof techniques based on formal logic and mathematical induction.
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SUMMARY OF COURSE CONTENT:
Proofs, Logic, and Sets: Basic concepts of mathematical proof, logic and proof techniques, conditionals, sets and set operations, Cartesian products, quanti fiers and their applications. We will spend some time also learning how to accurately represent written English statements in a mathematical way.
Integers and Modular Arithmetic: The integers, mathematical induction, divisibility, greatest common divisors and the Euclidean algorithm, primes and prime factorization, modular congruences and modular arithmetic. (If we have time, we will also look at the continued fraction algorithm.)
Relations, Orderings, and Functions: Relations, equivalence relations, partial and total orderings, functions, function composition, one-to-one and onto functions, inverse functions.
Cardinality and Countability: Bijections, cardinality of sets, countable and uncountable sets, the pigeonhole principle.
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LEARNING OUTCOMES:
Students will be able to write logically sound mathematical arguments and analyse such arguments. There will be no emphasis on memorising standard examples, but instead the students will develop their problem-solving and creative-thinking abilities.
The students will be prepared to move on to theory-laden mathematics and science courses that involve proofs and rigorous arguments, such as group theory, real analysis, theoretical physics, and theoretical computer science.
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TEXTBOOK:
| Book Title | Author | Publisher | ISBN number | Library Call Number | Comments | Format | Local Bookstore | Online Purchase |
| Mathematical Proofs: A Transition to Advanced Mathematics | Gary Chartrand, Albert D. Polimeni, Ping Zhang | ‎Addison-Wesley | 0201710900 | | Assignments will be provided. Many of the topics of the course can be found in various textbooks, if you do not want to buy this one, but I WILL NOT BE PROVIDING LECTURE NOTES. | | | |
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REQUIRED RESERVED READING:
RECOMMENDED RESERVED READING:
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GRADING POLICY
-ASSESSMENT METHODS:
| Assignment | Guidelines | Weight |
| Final exam | The final will be comprehensive, but with more problems on the material covered after the midterm. | 40% |
| Midterm | The midterm exam will be given at around week 7 or 8 of the course, and will cover all topics studied up to that point. | 30% |
| Homework assignments | Written assignments should be organized carefully, neatly, and in complete sentences, with concise well-reasoned logical arguments. On written assignments, you may work together with other people, but you must write up your work independently. If you use any external resources, including material found online, you must say what results you are citing and where they are from. If you find a solution to an assigned problem online or elsewhere, it is academically dishonest to copy the solution and present it as your own work. | 30% |
-ASSESSMENT CRITERIA:
AWork of this quality directly addresses the question or problem raised and provides a coherent argument displaying an extensive knowledge of relevant information or content. The student demonstrates complete, accurate, and critical knowledge of all the topics, and is able to solve problems autonomously.
BThis is highly competent level of performance and directly addresses the question or problem raised. There is a demonstration of some ability to critically evaluate theory and concepts and relate them to practice. The work does not suffer from any major errors or omissions and provides evidence that the student uses clear logic in their arguments.
CThis is an acceptable level of performance and provides answers that are clear but limited, reflecting the information offered in the lectures. Mathematical statements are properly written most of the time.
DThis level of performances demonstrates that the student lacks a coherent grasp of the material. Important information is omitted and irrelevant points included. Many mistakes are made in solving the problem raised. In effect, the student has barely done enough to persuade the instructor that they should not fail.
FThis work fails to show any knowledge or understanding of the subject matter. Most of the material in the answer is irrelevant.
-ATTENDANCE REQUIREMENTS:
Attendance is mandatory for the course.
You cannot make-up a major exam (midterm or final) without the permission of the Dean’s Office. The Dean’s Office will grant such permission only when the absence was caused by a serious impediment, such as a documented illness, hospitalization or death in the immediate family (in which you must attend the funeral) or other situations of similar gravity. Absences due to other meaningful conflicts, such as job interviews, family celebrations, travel difficulties, student misunderstandings or personal convenience, will not be excused. Students who will be absent from a major exam must notify the Dean’s Office prior to that exam. Absences from class due to the observance of a religious holiday will normally be excused. Individual students who will have to miss class to observe a religious holiday should notify the instructor by the end of the Add/Drop period to make prior arrangements for making up any work that will be missed.
DURING THE SEMESTER, MAKE-UP EXAMS WILL NOT BE GIVEN UNDER ANY CIRCUMSTANCES. If you need to miss an assessment, the weight of that assessment will be shifted to the final. If you have to miss the final, if you are in good standing with the course, you can ask for an incomplete. If you are not in good standing and miss the final, I will be unable to assign a grade for the course, other than by considering the class tests you have already completed (this means you will be assigned a D or an F as appropriate).
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ACADEMIC HONESTY
As stated in the university catalog, any student who commits an act of academic
dishonesty will receive a failing grade on the work in which the dishonesty occurred.
In addition, acts of academic dishonesty, irrespective of the weight of the assignment,
may result in the student receiving a failing grade in the course. Instances of
academic dishonesty will be reported to the Dean of Academic Affairs. A student
who is reported twice for academic dishonesty is subject to summary dismissal from
the University. In such a case, the Academic Council will then make a recommendation
to the President, who will make the final decision.
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STUDENTS WITH LEARNING OR OTHER DISABILITIES
John Cabot University does not discriminate on the basis of disability or handicap.
Students with approved accommodations must inform their professors at the beginning
of the term. Please see the website for the complete policy.
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SCHEDULE
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Weeks 1-2: Overview of Mathematical Proof, Propositions and Conditional Statements, Boolean Operators and Boolean Logic.
Weeks 3-4: Sets, Subsets, Intersections and Unions, Cartesian products and Quantifiers.
Weeks 5-6: Proof techniques, The Integers and Mathematical Induction with examples, Divisibility and the Euclidean Algorithm.
Week 7: Revision and Midterm
Weeks 8-9: Primes and Unique Factorization, Modular Congruences and Modular Arithmetic, Relations, Equivalence Relations and Ordering.
Weeks 10-11: Bijections, Cardinality, Countable and Uncountable Sets.
Weeks 12-13: The Pigeonhole Principle, Fields and the Real Numbers.
Week 14: Revision and preparation for the final.
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