代做Math 405: Real Analysis I Spring 2024帮做R语言

Math 405: Real Analysis I (Online)

Spring 2024

Overview: This course is an introduction to the basic tools of analysis and their applications to the calculus of functions of a single real variable. The material is developed in an online format and is administered using Canvas. In lieu of traditional class meetings, students interact with course elements virtually by viewing recorded lectures, attending synchronous review sessions, posting in discussion forums, and submitting requisite coursework.

Academic Objectives: By the end of the course, students will have:

• Developed the methods of mathematical proof necessary for a rigorous and sophisticated study of mathematics.

• Explored the properties of the real numbers and their subsets that are systematically used in analysis.

• Studied the essential notion of convergence and its applications to sequences, series, and functions.

• Revisited the major theorems of calculus from the enriched perspective of analysis.

• Used proper notation to communicate subtle mathematical ideas to themself, their classmates, and the instructor.

Course Prerequisites: A working knowledge of Calculus I is required, and that of Calculus II is preferred. Some practice with mathematical proofs is beneficial, but the needed techniques will be developed during the course. Most important is a willingness to refine one’s understanding of mathematics according to the new ideas and strategies we will encounter.

Course Structure: This 14-week online course is divided into eight modules. Modules and the course materials therein are released at Monday 12:01am ET of each week; students have until the following Sunday 11:59pm ET to complete the listed objectives. The following items appear in some or all of the modules.

Recorded lectures (weeks 1-14): Pre-recorded lectures motivate the week’s material, discuss definitions and theorems, detail important proofs, and reinforce understanding with worked examples.

Lecture notes skeleton (1-14): These notes contain the major definitions, theorems, ideas, and examples of the week. The student may, at their discretion, supplement the skeleton with the proofs and completed examples that are worked in the lectures.

Live Review session (1-14): At these synchronous meetings, the instructor will supplement the recorded lectures with more strategies and caveats. These sessions will be informal and tailored to the needs of the students; students who cannot attend live and provide instantaneous feedback to the instructor have the option of pre-submitting questions and comments which will be addressed at the meeting. All links to live meetings will be posted to Canvas, and the meetings will be recorded and posted for future reference.

Discussion forum (1-14): Students will interact with each other by use of the Canvas discussion board by answering prompts and responding to the answers of others. Each initial post is due by Friday 11:59pm ET; two responses to classmates are due by Sunday 11:59pm ET. More details about this course element will follow in the first week of the course.

Practice problems (1-14): This practice element is a “check your understanding”; the multiple choice questions therein concern basic definitions, theorems, and examples and are closely linked to the material presented in the lectures. This assignment is administered via Canvas. You have three attempts to complete the assignment; every attempt contains the same questions, and your highest score counts toward your course grade.

Quiz (1-14): There is a timed, 30-minute online quiz each week that tests your understanding of the week’s material. The questions therein are more involved and hint at more advanced ideas than those encountered in the practice problems. This assignment is administered via Canvas. You have two attempts to complete the assignment; each attempt randomly pulls questions from a question bank, and your highest score counts toward your course grade.

Problem set (1-14): The weekly problem sets are a primary vehicle of instruction for the course. The questions that comprise the problem set are designed to supplement the lectures by highlighting key ideas, clarifying confusing passages, and exploring deeper concepts. The problem sets are designed to be difficult!

Solutions to the assigned questions are to be neat, legible, and well-structured. It is not enough that you understand the solution strategy to a particular question; this understanding must be correctly formulated into a cogent mathematical argument. Usually, this requires that you revisit a problem set some time after you “solve the problem” to review your ideas and formalize them into a rigorous proof. At the start of the course, we will explore various proof strategies to help prepare you for this element of the course.

Reflection (1-14): You will write a brief reflection each week that accounts for your experiences as a mathematician. You may comment on what has been easy, list what still doesn’t make sense, attempt to summarize the material for the week, or do something totally different – as long as your journal entry documents an attempt by you to “learn how you learn”. Each week’s reflection need not exceed 150 words. They will be graded solely on the basis of completion.

Midterm Exams (6,12): There will be two 120-minute midterm exams. The date ranges are given below:

Midterm I: 7 March - 10 March

Midterm II: 18 April - 21 April

The exams are online and use Respondus Lockdown Browser and Webcam. The question format for the exam mirrors that of the quizzes. Notes, books, calculators, and electronic devices are prohibited during exams. Attendance to exams is mandatory; you must provide a letter from the Office of Academic Advising if you have a valid reason to miss an exam.

Project (7-14): There is an independent project in the second half of the course that enriches your understanding of topics developed in the lectures. The project focuses on problem solving and mathematical communication. More details about the project will follow as the course gets underway.

Final Exam (14): There is a cumulative final exam distributed in week 14 of the course. The date range is TBD. More details about the final will follow as the course gets underway.

Graded Elements: Your final grade for the course will be calculated using the following weighted average:

• Discussion forum: 5%

• Practice problems: 5%

• Quizzes: 10%

• Problem sets: 20%

• Reflections: 5%

• Midterm Exams: 2 × 12.5 = 25%

• Project: 10%

• Final Exam: 20%

In the event of an excused exam absence, your score for that exam will be calculated using a weighted average of your scores on the other exams. Unexcused exam absences will result in a score of zero. Letter grades will be assigned roughly on the following scale:

A: 90-100% B: 80-89% C: 70-79% D: 55-69% F: 0-54%

The instructor reserves the right to refine this scale as needed. Subgrades (“+” and “-”) will be determined at the end of the course.

Academic Accommodation: All students who require accommodation for the course should contact me at their earliest convenience to discuss specific needs. Students with documented disabilities or other special needs who require accommodation must register with the JHU Office for Student Disability Services.

Anonymous Feedback: I value all feedback about the course, including anonymous feedback. Addition-ally, I’m committed to ensuring that our course meetings value everyone’s inherent dignity. If you have academic suggestions or feel like you’ve been mistreated in this course, please contact me; if you feel un-comfortable doing so or prefer to remain anonymous, you can reach out to the Director of Online Programs (Joseph Cutrone), the Director of Undergraduate Studies (Richard Brown), or the Department Chair (David Savitt).

Attendance: Your attendance at live meetings is preferred, but not required; all such sessions are recorded for your viewing at a later date. Completion of the exams during exam windows is required.

Ethics: The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript. notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics.

You should collaborate with other students in this course on the general construction of problem set solutions. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please see the instructor.

For more information, see the guide on “Academic Ethics for Undergraduates” and the Ethics Board web site (http://www.ethics.jhu.edu).

Support: If you become stuck on a problem or concept, ask a classmate! I am also available for office hour consultation on a per-appointment basis; please do not hesitate to get in touch and set up a meeting.

There are many other sources of help and support if you encounter difficulty with the material. These include The Learning Den (http://www.advising.jhu.edu) and the Office of Academic Support (htpp: //www.academicsupport.jhu.edu).