MATH 210-01
Foundations of Mathematics
Syllabus for Fall 2009
Mon & Fri, 2:00 – 2:50pm
Wed, 2:00 – 3:50pm
329 Gildemeister Hall
Prerequisite: MATH 110 or MATH 120 or MATH 150 or a qualifying score on the mathematics placement exam
About This Course: Mathematics has two sides to it. The first side, sometimes called Computational or Applied Math, is one that you’re probably very familiar with. Almost all the classes you’ve taken so far have mainly focused on how to get an answer, whether it is a number, function, or an equation. This is the side of math that usually appeals to Engineers, Physicists, and other physical scientists who are looking for answers in the “real world.” The other side of mathematics is sometimes called Theoretical or Pure Math. In this area of mathematics the focus is on using deductive logic to construct and communicate sound, rigorous arguments while striving for abstraction and the recognition of underlying structure. This area of mathematics is beneficial to those who wish to study Law, Philosophy, Art, or, of course, higher Mathematics. MATH210 is meant to be an introduction to Pure Math and a precursor to the other Pure Math courses in the curriculum (specifically MATH330 and MATH440). In this course we will create a sound logical foundation “underneath” a lot of concepts (e.g. equivalences, functions, relations, numbers, etc.) with which you may already be familiar.
Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material, (ii) Perform logical computations and set manipulations, (iii) Demonstrate knowledge (i.e. memorization) of pertinent definitions and theorems, (iv) Reason deductively in a variety of forms, (v) Communicate mathematics correctly, clearly, and concisely.
Text: A
Transition to Advanced Mathematics
by Smith, Eggen, St. Andre, (6th Ed)
Course Website: http://course1.winona.edu/eerrthum/math210
Instructor: Dr. Eric Errthum Office: 124A Gildemeister Hall
Winona Email Username: eerrthum Office Phone: 474-5775
Office Hours: See schedule on my home page. Or by appointment on any day.
Grading:
Reading Quizzes (32 @
5 points, drop lowest 2) 150
points------ 15%
Quizzes (6 @ 25
points) 150
points------ 15%
Homework (scaled as
needed) 300
points------ 30%
Midterms (2 @ 100
points) 200
points------ 20%
Final 200
points------ 20%
-------
1000
points total
Grades: A = 90% (900 pts), B = 80% (800 pts), C = 70% (700 pts), D = 60% (600 pts). There will be no curving of individual exams, quizzes or assignments.
Reading Quizzes: Before every lecture, you are expected to complete a short (5 question) quiz on the assigned readings. You can find these quizzes by logging onto WeBWorK with your WSU username as your login and math210 as your password (feel free to change your password after logging in by clicking the “Password/Email” link to the left). Page numbers for the readings can be found in the schedule below. Reading quizzes are due 10 minutes BEFORE the class covering the material. There will be NO EXTENSIONS or MAKE-UPS. Your lowest 2 quiz scores will be dropped from your grade.
Quizzes: We will have 6 (approx. 25-minute) quizzes, one after each chapter. Each quiz will count for 25 points.
Homework: Homework will be assigned almost daily even if it is not specifically announced in class. See list of problems and due dates in the schedule below. There is a lot of homework assigned and that’s not because I’m trying to be mean. The most common thing in all of mathematics – I do it myself, as does every other mathematician I know – is to see somebody else doing a problem and say, “Yes, yes, of course. I understand completely,” and then walk away and realize that we had no idea at all what was going on. Homework is your guard against this. If you really understand how to do the homework, you're generally in pretty good shape. If you can't, you've got plenty of time to figure it out, ask me, ask a friend, or take whatever other action you see fit.
It is wise to work on the homework as it is assigned, for a couple of reasons. First, there will be enough of it that it will not be practical to just sit down and do the whole week's worth in an evening. Second, some individual problems will have to be thought about, played with, put down, and revisited. You must allow time for this. Third (and most importantly), the material builds on itself, so that a few days without working through at least some of the problems may find you feeling a little lost.
One of the main goals of this course is to improve your ability to communicate mathematics. Before you dive into the homeworks, I strongly advise reading the document “Writing Guidelines for All Assignments” so that you know what is expected of you.
LaTeX: Except for the first two sections, all homeworks are to be typed up in LaTeX using the homework template and handed in as a clean print-off. A variety of LaTeX resources can be found by clicking here.
Exams: There will be two in-class exams and one comprehensive final exam. Exam dates are tentative until officially announced in class. The final exam is scheduled for Wednesday, December 9, 10:30am – 12:30pm.
Resources: There is tutoring available in the Math Achievement Center on the first floor of Gildemeister Hall from 10am-3pm on Mondays through Friday and 5pm-7pm on Monday through Thursday. Beware: some of the tutors may not have had this class yet or had it with a different instructor using a different text. Also, you are encouraged to visit me in my office (see schedule on my home page, or by appointment on any day) or e-mail me. To be more clear: This might be a hard class for some of you. I'd like to see all of you do well in it. I'd love to talk with you and to help you in any way that I can.
Desire2Learn: Some course materials can be found on D2L including solutions to homeworks, activities, quizzes, and exams and approximate grades. If at any point during the semester you would like to know your exact grade, please email the instructor.
Late/Missed Work: Late homework or missed quizzes will result in a score of zero. Make-up quizzes and make-up exams will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.
Academic Dishonesty: Any type of academic dishonesty (cheating, copying, using a solutions manual to do homework, etc.) will result in failure and will be reported to school authorities. If you are having trouble, please see the instructor. You are allowed to work with others on your homework, but at the end of the day you must write your solutions in YOUR OWN WORDS.
Note: This syllabus is subject to change if deemed necessary by the instructor.
Tentative Schedule of Events – Math 210
(subject to change)
|
Week Beginning |
Monday |
Wednesday |
Friday |
|
8/24 |
READ: pp. x-xii, 1-6 Introductions 1.1 Propositions and Connectives HW: Go to the “Getting
Started with LaTeX” page |
BRING YOUR
LAPTOPS READ: pp. 6-8, 11-14 1.2 HW 1.1
(pg 8): 2df, 3hj, 4jn, 8a, 10bf Introduction to WeBWorK and LaTeX HW: LaTeX Assignment |
READ: pp. 14-17 HW 1.2 (pg 17): 2ce, 3d, 4dhj,
5fi, 6d, 9ad, 14a |
|
8/31 |
READ: pp. 20-24 LaTeX Assignment Due 1.3 HW 1.3 (pg 26): 1cek, 2cek, 4a, 6acef |
READ:
pp. 24-26, 28-33 HW 1.4 (pg 37): 3cde, 5be, 6ab, 7cgik, 11b |
READ: pp. 32-36 |
|
9/7 |
NO CLASS |
READ: pp. 39-44 HW 1.3 & 1.4 Due 1.5 HW 1.5 (pg 44): 1bd, 3bcf, 5b, 7b, 11, 12acd |
READ: pp. 47-52 HW 1.6 (pg 53): 1bg, 3, 5de, 7gij, 8ceh |
|
9/14 |
READ:
pp. 51-53, 56-64 HW 1.7 (pg 64): 1a, 2b, 6a, 12def |
READ: pp. 69-75 HW 1.5 – 1.7 Due Question & Answer Period Chapter 1 QUIZ 2.1 HW 2.1 (pg 76): 4bdfhl, 8abcd, 9bdfhjl, 11, 16, 19abd |
READ: pp. 78-83 HW 2.2 (pg 83): 1bdhj, 3acemn, 4bce, 10bef, 14df, 15bd, 17cfg |
|
9/21 |
READ: pp. 86-92 HW 2.3 (pg 92): 1hjkn, 6b, 10b, 14, 17d, 20cde |
READ: 96-101 2.4 HW 2.4 (pg 106): 5cd, 8dfjlq, 9f, 15cdf Worksheet (Inducting on Dominos) |
READ: pp. 101-105 |
|
9/28 |
READ: pp. 110-115 HW 2.5 (pg 116): 2, 3a, 6b, 12b, 15acd |
HW 2.4 – 2.5 Due Chapter 2 QUIZ Chapter 1 and 2 Review |
EXAM I |
|
10/5 |
READ: pp. 131-137 HW 3.1 (pg 142): 4abc, 5abc, 6bdfg, 15, 20cefg |
READ:
pp. 137-142 READ: pp. 145-150 HW 3.2 (pg 150): 1bfi, 4acf, 7ef, 12ac, 13, 16abd |
Exam I Solutions |
|
10/12 |
READ: pp. 154-157 HW 3.3 (pg 158): 3ac, 6c, 10ab, 15abc |
READ: pp. 179-180 HW 4.1 (pg
185): 3befj, 6ad, 8cd, 18abde Worksheet (Creation of the Rationals) |
HW 3.1 – 3.3 Due Chapter 3 QUIZ |
|
10/19 |
SICK DAY |
READ: pp. 189-195 HW 4.2 (pg 195): 3bfg, 8, 11, 18, 19bcd The mini-Snake Lemma… Prove it! |
HW 4.1 & 4.2 Due HW 4.3 (pg 205): 1dfij, 2dfij, 4, 14ab, 17bdgh |
|
10/26 |
READ: pp. 203-204, 208-211 4.3, cont. HW 4.4 (pg 211): 2bd, 11b, 14bef, 20, 22bc |
HW 4.3 – 4.4 Due Chapter 4 QUIZ Chapter 3 and 4 Review |
EXAM II |
|
11/2 |
READ: pp. 221-228 HW 5.1 (pg 228): 5bdfgk, 6b, 10,
17ab, 21ac |
READ: pp. 230-235 HW 5.2 (pg 235): 1cg, 2f, 9, 12be Exam II Solutions |
READ: pp. 237-244 HW 5.3 (pg 245): 3, 8ab, 12abc,
16bcd |
|
11/9 |
READ: pp. 247-253 5.4 HW 5.4 (pg 253): 3, 5cd, 7, 15c, 17ac |
READ: pp. 254-258 (No lecture on this material) NO CLASS |
HW 5.3 – 5.4 Due Chapter 5 QUIZ |
|
11/16 |
READ: pp. 261-266 HW 6.1 (pg 266): 9a, 14ac, 15b, 16ac |
READ: pp. 269-274 HW 6.2
(pg 274): 1d, 9ab, 11, 20ad Group Activity |
HW 6.1, 6.2 Due HW 4.5 (pg 218): 4be, 8bd, 9a |
|
11/23 |
Construction of the Reals |
NO CLASS |
NO CLASS |
|
11/30 |
READ: pp. 300-304 HW 7.1 (pg 304): 1hgci, 4b, 5a, 18acde |
HW 4.5 & 7.1 Due Chapter 6 & 7.1
& 4.5 QUIZ Chapters 1 – 4 Review |
Chapters 5 – 7 Review |
Final Exam
Wednesday, December 9
10:30am – 12:30pm
Welcome to college math!
If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.
#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”
#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.
#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.
#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.
#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.
#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.
#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.
Good luck on a happy and successful semester!
Commitment to Inclusive Excellence: WSU
recognizes that our individual differences can deepen our understanding of one
another and the world around us, rather than divide us. In this class, people
of all ethnicities, genders, religions, ages, sexual orientations,
disabilities, socioeconomic backgrounds, regions, and nationalities are
strongly encouraged to share their rich array of perspectives and
experiences. If you feel your differences may in some way isolate you
from WSU’s community or if you have a need of any specific accommodations,
please speak with the instructor early in the semester about your concerns and
what we can do together to help you become an active and engaged member of our
class and community.
Campus
Resources
·
Student
Support Services, Howell Hall 133, 457-5465 (www.winona.edu/studentsupportservices/)
·
Inclusion
and Diversity Office, Kryzsko Commons Room 122,
457-5595 (www.winona.edu/culturaldiversity/)
·
·
·
Writing
Center, Minné Hall 348, 457-5505 (www.winona.edu/writingcenter/)
·
GLBTA
Advocate, Wabasha Hall 220, 457-5330 (www.winona.edu/counselingcenter/)
·
Advising
and Retention, Maxwell 308, 457-5600 (www.winona.edu/advising/)
Details about Campus Resources
·
Two
good places to help you find resources of all kinds on campus are Student
Support Services and the Inclusion and Diversity Office. Both offices are
dedicated to helping students of all races, ethnicities, economic backgrounds,
nationalities, and sexual orientations. They can facilitate tutoring and
point you to a wide range of resources. Student Support Services is in
Howell Hall 133, and they can be reached at 457-5465. The Inclusion and
Diversity Office is in Kryzsko Commons Room 122, and
they can be reached at 457-5595.
·
If
you have a disability, the Disability Resource Center (DRC) can document it for
your professors and facilitate accommodation. Their office is in Maxwell Hall,
3rd floor, and they can be reached at 457-2391. If you have a
documented disability that requires accommodation, please let me know as soon
as possible. If you suspect you may have a disability, you are encouraged to
visit the DRC as soon as possible.
·
College
can be very stressful. The
·
For
help with writing and the development of papers, the English department has a
·
The
GLBTA Advocate is responsible for documenting homophobic incidents on campus
and working with the appropriate channels to get these incidents resolved. In addition,
the advocate can direct people to GLBT resources on campus and in Winona.
Contact the Counseling Center for the name and number of the current GLBTA
Advocate. (Wabasha Hall 220, 457-5330)
The Standard Disclaimer
applies.