Instructor	Anand Pardhanani Email: pardhan@earlham.edu CST 210 Phone: 765-983-1683
Office hours	The following hours are tentative - I'll finalize office hours after the 1st week         M: 10-11am.   T: 10-11am.   W: 10-11am.     And by appointment or walk-in. The best way to contact me, in order of preference, is: [1] in person,   [2] by email,   [3] by phone. Open door policy: I keep my posted office hours to a bare minimum, to avoid being locked into a rigid schedule all semester. However, I am happy to assist students well beyond my office hours. Students are encouraged to just drop by whenever needed. Anytime my office door is open you're welcome to stop by and check whether I am available. Also, please do not hesitate to make an appointment if my posted office hours don't work for you.
Class website	https://cs.earlham.edu/~pardhan/courses/intro_proof/   The website is a central component of this class, and you are responsible for regularly checking it for announcements, homework assignments and various supplementary handouts. I prepare for class with the assumption that students have reviewed the website and followed through on posted instructions.
Textbook   Write Your Own Proofs in Set Theory and Discrete Mathematics, by Amy Babich and Laura Person, Zinka Press, 2005.   (ISBN: 0-9647171-7-4) It is also available in the form of a Dover publication, 2019. (ISBN13: 978-0486832814)
Course credits   This course is worth 4 credits, and will meet for in-person classes 8 hours each week for 7 weeks. This is consistent with the standard practice of 4-credit courses meeting for 4 hours per week during a regular 14-week semester. In addition, students should expect a workload outside class of about 15 hours each week.
Requirements this class fulfills   This class is required for majoring or minoring in math. It is also a prerequisite for MATH 420 (Abstract Algebra A) and MATH 430 (Analysis A). In addition, it fulfills the writing requirement in math, plus the Abstract Reasoning (AR) component of Earlham's General Education requirements.
Description & objectives   This course is unique in that its central goal is to teach mathematical language and process, rather than mathematical content. It is designed to help students transition to higher mathematics, and to prepare for upper level courses in the major sequence and beyond. To accomplish this overarching purpose we will focus on a set of key foundational topics, together with learning the language and process for constructing abstract mathematical solutions and proofs. By the end of this course you will be on the path to becoming a producer of mathematical knowledge as much as a consumer of it. Although we will learn some new mathematics along the way, our emphasis throughout the semester will be on learning and refining how we do mathematics, and how to communicate mathematical content. Thus, you will be expected to pay careful attention to details, and to develop solutions that are not only correct, but are also rigorous and complete. In many ways, this class is very similar to a foreign language class! To succeed, you will need to memorize vocabulary (e.g., definitions) and the rules of grammar (e.g., logic & key theorems). You will also need to learn to put them together to write meaningful prose (e.g., to write proofs).
Student learning goals and outcomes   Upon successful completion of this course, students will be able to   1.   Understand deeply the basic principles of logic and a range of standard proof techniques used in mathematics.   Why this goal? Mathematical logic is special in that the outcome of logical analysis is independent of who the logician is. Qualities such as intelligence or "IQ" that are often associated with logical reasoning in other areas of life play no role in determining the outcome in mathematical logic. Only systematic and correct application of the rules of logic matters, and it leads everyone to the same end result. In turn, these rules of logic comprise the foundation of proof techniques used in mathematics.   2.   Apply those techniques in the context of essential mathematical structures such as sets, relations (including orderings and equivalence relations), functions, etc.   Why this goal? Although advanced mathematics consists of a mind-bogglingly diverse range of ideas, most of these are built upon the foundational concepts of set theory, relations, functions, and other similar building blocks.   3.   Gain comfort working with definitions, theorems and other abstraction strategies used in mathematics.   Why this goal? Whether you are learning, exploring or communicating mathematics, the use of definitions, theorems and abstraction strategies is indispensible to all of these enterprises. They comprise the backbone of the language of mathematics.   4.   Develop rigor, clarity and precision in mathematical reasoning, communication and proof-writing skills.   Why this goal? To cultivate the discipline and habits of mind that will help the student transition smoothly and successfully into becoming a learner of advanced mathematics. 5.   Use the LaTeX suite of software tools to typeset and publish professional quality mathematical writing.   Why this goal? A key challenge in typesetting mathematical writing is the ubiquitous need to include symbols, equations, and various other mathematical objects (vectors, matrices, arrays, etc.). LaTeX not only provides an exceptionally high-quality, open-source technology framework to meet these needs, but it also continues to be widely used for mathematical writing throughout the world. In fact, most mathematics periodicals, journals, and conference organizers require all documents submitted for publication to be typeset using LaTeX. These aspirations broadly support all 5 learning goals of the Math Department, and the 7 goals of an Earlham education (see the Appendix attached to this Syllabus).
Course prerequisites: Mathematical Discovery (MATH 190).
Assessment & grading policy  Your final grade will be based on combined performance on: quizzes and classwork, writing assignments, homework problems, one exam during the semester, and a final exam. Each will contribute the following proportions: Quizzes & Classwork 30% Writing portfolio 15% Homework 15% Mid-term exam 20% Final exam 20% Letter grade boundaries for this course are not set in advance. They will be determined at the end of the term, based on factors such as overall class performance, level of difficulty of tests, quizzes, and assigned work, etc. At a minimum, the following standard scale for letter grades will be honored:         A+: 97.0-100;   A: 93.0-96.9;   A-: 90.0-92.9;         B+: 87.0-89.9;   B: 83.0-86.9;   B-: 80.0-82.9;         C+: 77.0-79.9;   C: 73.0-76.9;   C-: 70.0-72.9;         D+: 67.0-69.9;   D: 63.0-66.9;   D-: 60.0-62.9;   F: below 60. NOTE that all students must also satisfy the following minimum requirements to receive a grade of C- or better:         * Take both the exams (mid-term and final).         * Turn in at least 75% of the homework problems.         * Turn in at least 75% of the quizzes and classwork.         * Turn in a complete writing portfolio.
More details about assessment categories   Quizzes and classwork:  In-class quizzes and/or classwork will be frequently assigned throughout the semester. A key purpose of the quizzes is to help us accomplish learning goals 1 and 3 (listed above). Often, a quiz will simply ask for a complete and mathematically formal statement of a defintion or a theorem, or to apply a formal rule of logic to some given situation. Classwork, on the other hand, will be much like homework problems, and will serve the purpose of hands on learning and practice in class. This will help us accomplish learning goals 1 through 4. Students will sometimes do classwork in teams and, in such cases, turn in a common "team solution" for grading. Writing portfolio:  A key goal of this class is to help you learn to clearly, precisely and completely express mathematical solutions in writing. With this in mind, I will periodically assign proofs on which students will need to do multiple rewrites in an effort to attain perfection. Your writing portfolio will serve as the mechanism to facilitate and keep a record of your work. The grading of portfolio work will strongly consider written aspects of your proof, together with its mathematical content. In particular, I will carefully assess your usage of both English and mathematical grammar, and whether you really said everything that was needed to make your solution correct and complete. The writing portfolio will be particularly helpful for accomplishing learning goals 2, 4 and 5. Homework:  The purpose of homework is to help you learn mathematical content and to give you practice with proof strategies and other solution techniques. Exercises will be assigned from the textbook and other sources at various points throughout the semester. These must be turned in at the beginning of class on the indicated due dates. Homework exercises will help us accomplish learning goals 1 through 4. Exams:  There will be one mid-term exam during the term, plus a final exam at the end of the term. The exams will help fulfill and assess goals 1 through 4. The tentative date of the mid-term exam is August 27. The final exam date and time is set by the registrar's office. According to their calendar, the final exam will be held Monday, Sep. 27, at 1 pm.
Important dates         *   Last day to add this course: August 11.       *   Last day to drop: Sep. 10.       *   Date of final exam: Sep. 27. NOTE: Last drop date applies to Earlham students only. Students cross-registered through IU-East or other institutions must follow the dates and rules of their own institution.
Academic integrity   After several years of writing standard, boiler-plate stuff in this section, I have decided to replace it with a more authentic message from my heart to yours. Before getting into details, I would like to share 3 key ideas that profoundly shape my thinking, and prompt me to explore more effective ways towards academic integrity: Academic infractions are a much bigger problem at Earlham than many of us would like to believe or admit. The problem is NOT our students! Earlham students are as good (or better!) than their peers at other institutions in terms of moral values and ethical standards. Infractions at Earlham can be significantly reduced using a combination of strategies, collectively developed by students and faculty. These three points summarize my overall perspective, and will frame the rest of my discussion on this subject. By far the single biggest phenomenon that has radically transformed today's academic integrity / infraction landscape is technology -- particularly the internet and cell phones. In my view, Earlham's traditional approach to academic integrity has been rendered completely obsolete by these technologies. If I were an Earlham student today, I would encounter many situations where the temptation to infract would be extremely high, because these technologies make it so easy, and the risk of getting caught is virtually zero. This is the main reason why I say that you, the student, are not the problem. You are human, just like me and my faculty colleagues. It is a fact of life that many humans succumb to temptation when the rewards are sufficiently high, and the risks sufficiently low. Yet, the fact remains, a growing rate of academic infractions is a terrible thing to ignore: They sink an institution's reputation, decrease the value of students' education, lower student & faculty morale, and more. Clearly, we need to explore and develop new strategies that are more effective for our times, and also preserve Earlham's distinctive approach to such matters. We will set aside some class time to discuss and formulate specific policies for helping students (joyfully!) meet and exceed the highest standards of integrity in this class. In the meantime, I invite you to reflect on some practical ways that would most help and support you in avoiding the use of inappropriate sources for completing and turning in your graded work. I would like to conclude with the following excerpt from the Earlham Academic Integrity Policy: "The College trusts students who enroll at Earlham to be honest seekers of truth and knowledge. This trust is extended to all students by other students and by teachers ...   Giving or receiving aid inappropriately on assignments and tests, or plagiarizing by using another person's words or ideas without credit, constitutes a serious breach of our trust in one another and in the integrity of the search for truth. Those who believe they have witnessed violations of academic integrity should feel the obligation to speak about this to the suspected offender. The witness also should feel obligated to report the suspected offender to the instructor if the person fails to offer a satisfactory explanation and refuses to report him or herself. ...   Violations of academic integrity, because they undermine our trust in one another and in the credibility of the academic enterprise, are taken very seriously. Penalties for violations range from failing assignments or tests to suspension or expulsion from the College. "
Makeups   In-class items: There will be no makeup for missed in-class items (e.g., quizzes, classwork, class participation, etc.) regardless of reason. I will drop your lowest two scores as an implicit way of making up for missed items. Homework: Past-due assignments will not be accepted except in rare circumstances, provided the student receives prior consent from the instructor. Exams: Make-up exams will not be given except in cases of documented illness or emergency.
Academic accommodations   Students with a documented disability (e.g., physical, learning, psychiatric, visual, hearing, etc.) who need to arrange reasonable classroom accommodations must request accommodation memos from the Academic Enrichment Center (main floor of Lilly Library) and contact their instructors each semester. For greater success, students are strongly encouraged to visit the Academic Enrichment Center within the first two weeks of each semester to begin the process. For further details, please visit https://earlham.edu/academics/academic-support-and-special-programs/academic-enrichment-center/accessibility-services/
Other sources of help   The Academic Enrichment Center: The Academic Enrichment Center (AEC), located in Lilly Library, provides assistance with study habits and skills as well as a peer tutoring service. The AEC is staffed by trained peer tutors for either pre-arranged group tutoring sessions (provided for many math, science and social science courses) or one-on-one tutoring sessions for other courses. Peer tutoring is a free service offered to all Earlham students. Please visit https://earlham.edu/academics/academic-support-and-special-programs/academic-enrichment-center/peer-tutoring/ for more information. The Earlham Writing Center: The Writing Center is dedicated to providing students with advice and resources about writing. Students can meet one-on-one with trained consultants who will contribute feedback to writers at any stage of the writing process: brainstorming, drafting, researching, revising, and polishing. This is a free, walk-in service on the main level of Lilly Library. In addition to dropping by, students may also schedule an appointment in advance using the online scheduler found at: http://www.earlham.edu/writing-center/. Also, if you want help with specific grammar topics related to your own writing, https://www.grammarly.com/edu is available for all Earlham students to proofread their papers and learn more about grammatical errors.