A Survey of Mathematical Reasoning is a liberal arts mathematics course which provides insight into nature of mathematical reasoning by examining basic structures such as logic, sets, real numbers, numeration systems and inductive reasoning.

Upon successful completion of this course, students should be able to:

• distinguish between deductive and inductive reasoning and be able to apply each in problem solving;
• make connections between mathematical discoveries and the history of human thought;
• perform the basic operations of set theory, including: intersection, union and complement;
• analyze basic data-type questions (survey results) using subsets and Venn diagrams;
• translate verbal statements into symbolic forms of implication, conjunction, disjunction and biconditional;
• test for the validity of arguments using various methods, indirect as well as direct;
• define logical connectives using truth tables and be able to discover tautologies and prove theorems using truth tables;
• convert to any base using expanded numeral concept as well as the division algorithm;
• distinguish between rational and irrational numbers using the infinite decimal concept (OPTIONAL);
• solve problems on a calculator or computer involving loans, interest, mortgages, annuities and life insurance (OPTIONAL);
• analyze switching circuits using logical equivalences; (OPTIONAL);
• write computer programs using proper structured programming techniques (OPTIONAL);
• diagram the logical design of a computer or calculator (OPTIONAL);

1. Core Topics:
   1. Logic (Math thinking) (3–5 weeks)
      1. Deductive thought
      2. Inductive thought
      3. Conjecture, proof
      4. History of logic
      5. Definitions: arguments, validity, theorems, truth tables, proofs (direct and indirect)
   2. Sets (2–3 weeks)
      1. History
      2. Definition
      3. Operations with sets
      4. Venn diagrams, survey problems
      5. Arguments, theorems, proof, conjecture (OPTIONAL)
      6. Cardinal numbers (OPTIONAL)
      7. Infinite sets (OPTIONAL)
      8. Finite sets
      9. Equivalent sets
      10. One-to-one correspondence
      11. Cantor's theorems (OPTIONAL)
2. Additional Topics (at least three, 2–3 weeks each):
   1. Real numbers
      1. Natural numbers
      2. Integers
      3. Rational numbers
      4. Irrational numbers
      5. Properties of the systems (closure, etc.)
      6. Calculators: History, Algorithms, Order of operations
   2. Switching Circuits
      1. Definitions
      2. Problems
      3. Theorems
   3. Boolean algebra
      1. Definitions
      2. Theorems
      3. Proofs
   4. Numeration system
      1. Historical
      2. Positional
   5. Number Bases
      1. Unique representation
      2. Other than 10 bases
      3. Connecting to other bases
      4. Application to computer
   6. Inductive Reasoning
      1. Find the $n$-th term of a sequence
      2. Prove sum of arithmetic and geometric series
   7. Computers
      1. History
      2. Processing
      3. Flow chart
      4. Programming

This class will be conducted in the traditional format of face-to-face lectures. When taking this class, students must:

• attend the class, as scheduled;
• actively participate in class work;
• prepare assigned reading;
• submit assigned homework;
• take and pass all the in-class quizzes and the final exam.

Make-up tests will be given only for documented emergencies, and then only at the instructor's discretion and convenience. However, if you have a good reason, please do ask for consideration.

The class will be conducted in real time, face-to-face, in the format of a traditional lecture,

You are expected to attend every class session. You are responsible for all that transpires in class (including content, course requirements, tests and assignments) whether or not you are in attendance, even if your absence is the result of late registration, add/drop activity at the beginning of a term as permitted by College policy, or religious observance.

Arriving late, leaving early or taking unreasonably long breaks counts as partial absence.

The College defines excessive absence or lateness as more than the equivalent of one week of class meetings during the semester. Excessive absence or lateness may lead to failure in, or removal from, the course. You may be required to drop or withdraw from this course when, in the judgment of the instructor, your absences have been excessive.

In accordance with the New York State Education Law §224-a, any student who is unable to register or attend class on a particular day because of religious observance will be excused from any examination, study or work requirement scheduled for that day. Students must notify the professor, via College email (or otherwise in writing), at least one week prior to their absence due to a religious observance. In that case, students shall be given an equivalent opportunity to make up any examination, study, or work requirements within a reasonable amount of time of the religious observance. Please refer to the Religious Observance Policy for additional information.

• Don't hesitate to ask a question right away while in class — this class will encourage and facilitate immediate feedback.
• Come to the instructor's office hours.
• Use free online or in-person tutoring at the Academic Tutoring Centers. All tutoring sessions are offered by appointment only. Appoimtments are done online through WCOnline system.
  1. To create a WCOnline account: go to https://sunysuffolk.mywconline.net/register.php, and complete the registration form using your Suffolk email address and a 10-plus character password (other than the one you use for SUNY Suffolk).
  2. To make an appointment:
     1. Login to your WCOnline account at https://sunysuffolk.mywconline.net/index.php;
     2. Select Math Tutoring - Spring 2025 from the "AVAILABLE SCHEDULES"; The schedule is color-coded as follows: 
        • White blocks = Available;
        • Dark blue blocks = Not available;
        • Bright blue blocks = Other appointments;
        • Yellow blocks = Your in-person appointments;
        • Green blocks = Your Zoom appointments.
     3. Click on a white box of your choice. Each white box is a 30-minute or 45-minute session depending on the subject. Complete the appointment pop-up form by choosing whether you would like a Zoom or in-person session. You can also upload any documents you would like to share with the tutor.
     4. Click ‘CREATE APPOINTMENT’. If prompted, use the course MAT101 – A Survey of Mathematical Reasoning and instructor Alexander Kasiukov.
     5. After scheduling an appointment, check your Suffolk email for confirmation. 
     6. Be on time. Please allow time for technical difficulties and contact us if they occur. If you scheduled a Zoom appointment, the tutor will email you the Zoom information before the session. In-person appointments will meet at your scheduled time at the Academic Tutoring Center located in the Learning Resource Center (LRC-149) on the Grant Campus. Vaccination is required for in-person tutoring.
  3. To join the waiting list: if a session you would like to attend is filled, you can join the waiting list. Click on the link link at the bottom right of each day on the schedule  and fill in the pop-up form. If an appointment opens up, a notification will be sent to you via text or email.
  4. To cancel an appointment
     1. Login to your WCOnline account at https://sunysuffolk.mywconline.net/index.php;
     2. Click on your appointment box and click on the 'CANCEL' button. As a courtesy to your tutor and other students, we ask that you cancel appointments at least 2 hours before the session. This will allow time for another student to schedule that session.  If you do not cancel within that time, it will be counted as a missed (no show) appointment. After 3 no shows, your account will be deactivated. 
  5. To contact the Center: email at tutoringcenterwest@sunysuffolk.edu or call (631) 851-6369.

  In-person tutoring takes place in Learning Resource Center, Room 149. Up to 8 people can be scheduled for the same in-person time slot.

• Use the college library online or in person.
• Use computers available in the Academic Computing Centers / Computer Labs.
• Get counseling and advising at the Counseling Centers. The Grant Campus Counseling Center is located in Caumsett Hall, Lower Level, Room 20 and can be reached at (631) 851-6250.
• If you need support related to your psychological, emotional or social well being, Mental Health and Wellness Services provide free and confidential counseling. You can contact the Services at mentalhealth@sunysuffolk.edu or call to speak with a Michael J. Grant Campus counselor at (631) 851-6876. The Grant Campus office is located Sagtikos Building, Room 122.

Disruptive behaviors, as defined by the Student Handbook, will not be tolerated. In case of violations, the college policy allows the instructor "to remove a student from a class for one class meeting, and, in those cases where the continued presence of the student poses a substantial threat or would be disruptive to the class, request that the Associate Dean of Student Services impose an interim suspension pending a disciplinary hearing."

Suffolk County Community College provides students with the opportunity to demonstrate their knowledge by submitting coursework that is uniquely theirs and giving proper attribution to the work of others. Participating honestly in the SCCC academic community ensures that students can take pride in their education and their contributions to scholarship. Without academic integrity, students gain unfair advantage over others and prevent their own intellectual progress. As a student in this class, you are expected to uphold the SCCC core value of integrity and understand the Special Procedures for Academic Dishonesty (section P. starting on page 23 of the Student Code of Conduct). Specifically, when academic integrity is violated, the college policy allows the instructor to "initiate student conduct action through the Campus Associate Dean of Student Services. The faculty member may impose any of the following penalties: require that the student repeat the assignment or the exam; give the student a failing grade for the assignment or exam; or give the student a failing grade for the course. Should the student believe that s/he has been wrongly or unfairly accused of academic dishonesty, the student shall have the right to pursue the matter though the Course Grade Grievance Procedure."

The Code prohibits academic misconduct, which includes any action that results in students giving or receiving unauthorized assistance in an academic exercise, or receiving credit for work that is not their own. Academic exercise includes all forms of work submitted for credit. Academic misconduct includes, but is not limited to, the following behaviors:

• cheating — unauthorized use of textbooks, notes, mobile devices, artificial intelligence tools or any other sources;
• plagiarism — use of another person's work or ideas without crediting them, including using material generated by artificial intelligence tools for an assignment without instructor authorization;
• complicity — giving help to, or receiving help from, someone engaged in academic misconduct;
• multiple submissions — submitting the same work for credit in more than one course without the instructor's permission;
• falsification and forgery — making up information or falsifying your own or someone else's identity.

Information about the Student Code of Conduct, plagiarism and the citation process can be found on the Academic Integrity Procedures webpage. To learn more about academic integrity, college policies and expectations in this area, and proper ways to avoid possible violations, see the Academic Integrity and Plagiarism Guide.

Suffolk County Community College provides reasonable accommodations to registered students with disabilities who have self-identified and been approved by the Office of Disability Services. Once approved for reasonable accommodations, such students will be provided with an Accommodation Letter, describing the specific accommodations. Students must present this letter to each of their professors before accommodations can be provided.

Students who have, or think they may have, a disability are invited to contact Office of Disability Services for a confidential consultation. You can call the Office at (631) 851-6355, contact it via email disabilityG@sunysuffolk.edu, or stop by to make an appointment in Caumsett Hall, Lower Level, Room 20.