Modern Geometry

Professor Hlas
hlascs (@) uwec.edu
Drop-in hours / Zoom appointments

Each problem I solved became a rule, which served afterwards to solve other problems.
Rene Descartes

Course Information

This course focuses on axiomatic thinking in Euclidean and non-Euclidean geometries. Emphasis will be on proof techniques, finite geometries, Euclidean constructions, transformations, spherical geometry, hyperbolic geometry, and geometry software.

Goals

Course structure

Required

  1. Geometry & Symmetry by Kinsey, Moore, & Prassidis, 2011
  2. Euclid Elements (with applets)
  3. Geometry software

Research background


Grading

It is important to accurately show your mathematical thinking and to communicate clearly. If any concerns arise regarding grading, contact the instructor outside of class time. Students earn "math points" (MP) for demonstration of mathematical thinking in their solutions.

Warm-up activities

Warm-up activities is often assigned to prepare students for in-class activities. These activities are more effective when everyone attends class fully prepared. "Eyeglasses" in the calendar will indicate warm-up activities.

Recommended practice

Explicit homework is usually not given to practice course material. Instead it is recommended to:

Wikibook author (3 × 10 MP)

Most class activities will require updating the wikibook. A student from each group will volunteer for that class's updates. See the score sheet for more information.

Group quizzes (8 × 10 MP)

Each group will submit one quiz and each member of that group will receive the same score. Students are expected to fully contribute to quiz solutions and quiz items may appear on examinations. Quizzes will typically have an application problem and require a proof.

Projects (2 × 20 MP)

Student projects will extend what is discussed in class. The first project will be as a group, the second project will be individual. More details will be discussed when appropriate.

Exams (2 × 25 MP)

"To assess conceptual knowledge, researchers often use novel tasks … Because children do not already know a procedure for solving the task, they must rely on their knowledge of relevant concepts to generate methods for solving the problems." (Rittle-Johnson, Seigler, Alibali, 2001, p. 347). A such, assessments are a part of the learning experience and will not only require mastery of class material, but will also require the ability to apply class material to new situations.

For each exam, note sheet (1 page, 1-sided, handwritten) is allowed.

Final exam 30 MP

Cumulative final exam following same structure as in-class exams.

Bonus (? MP)

Homework, quizzes, or examination points may be assigned beyond those indicated above.

Tips for a successful semester 👍

The course schedule is your friend. I continually update it to make sure it is always as current as possible. All class activities, handouts, and daily recommendations should be listed. If something is missing or unclear, please let me know so I can make improvements for the benefit of everyone in the class. Speaking of calendars, the one thing I wish I knew as a college student is to schedule study time for each class. This strategy ensures time is spent on each classes in productive ways.

Mathematics is a form of abstract thinking that is better learned through active participation. In one study (Deslauriers et al., 2019), students were either taught via lecture or through active learning. Students in the lecture class felt like they learned more, but they actually scored lower than the active learning group. Active learning means that class will often begin with a challenging problem. During class the students and the instructor will work together to solve the problem(s) and learn some mathematics along the way (Liljedahl, 2017; Brown et al., 2014; Ericsson, 2006).

One way to actively engage with mathematics is to try homework or Webwork before class discussion on the topic. This strategy helps inform your learning during class time because you will have an idea of what you know and what you still need to learn (Pan & Sana, 2021; Brown et al., 2014).

When solving problems do not expect perfection. Problems are designed to be challenging to encourage learning. Little, if anything, is learned from "easy" tasks. Speaking of learning, we will try to avoid tricks/shortcuts as these often distract us from the mathematics and create extra work to unlearn the bad habit.

After each class, educational research recommends we reflect on what was learned. One way to review is to rewrite class notes. For a specific note-taking suggestion, please see the Feyneman's Notebook Method that encourages rewriting a day's lesson with a one-page restriction. Hand-written notes also lead to more brain activity than other methods (Umejima et al., 2021; Askvik et al., 2020; ScienceDaily, 2011).

Another method for review is to focus on activities with immediate feedback. For example, WeBWorK, flash cards, study groups and practice testing all have elements of formative feedback that is immediate (Weimer, 2017; Dunlosky, 2013; ScienceDaily, 2013; Butler et al., 2008; Ericsson, 2006).

Frequently Asked Questions (FAQ)

When/how is the professor available outside of class?

Email is the best way to reach me. I typically respond within 24 hours, but I do not check email in the evenings or on Saturdays.

My student drop-in schedule and sign-up for Zoom appointments are posted at https://math.hlasnet.com/officehours

What is the attendance policy?

A record of attendance is required by the University to maintain accurate class rosters. Attendance is not graded but poor attendance may impact participation in group activities (e.g., taking a group quiz individually).

If you are absent, please check the course schedule then meet with the instructor via drop-in hours, Zoom, or email to make sure you are caught up. Graded work that occurs during an authorized absence (school functions, emergencies or illness) may be made up for full credit. Other absences may complete graded assignments late for 90% credit or these assignments may be completed early for full credit.

Late work is expected to be completed within two weeks of the return date or by the last day of classes, whichever occurs first. In situations where a makeup cannot occur, the final exam score may be used as a proxy for a missing assignment. Students missing a week or more of class should contact the Dean of Students Office to get extra support.

What if I am stressed out?

College can be difficult. After all, if it wasn't then you likely are not learning very much. Everyone can benefit from placing their personal well-being as a top priority throughout the semester. Should you want some emotional support for any reason, you can access free counseling services (even one short session to problem-solve solutions) from the UWEC Counseling Services on campus. They provide a variety of online and in-person services, including some virtual wellness workshops. Call them at 836-5521, stop by Old Library room 2122, or check out the website to make an appointment: https://www.uwec.edu/counseling-services/

Students also have FREE access to UW System Mental Health Support through Mantra health – a telehealth service available 24/7 days a week (call or text: 888-531-2142 or go online at: app.mantrahealth.com; sign up using your UWEC email address). You can also reach out to the WI-branch of the national crisis/emotional support text line by texting "HOPELINE" to 741 741 or use the national suicide prevention lifeline: 988 Please use these resources to support your mental well-being and success as a Blugold!

What if the math class is too easy or too difficult?

The Department of Mathematics also allows students within entry-level mathematics courses (i.e., 010, 020, 104, 109, 112, 114, or 246) to move up to a higher numbered course during the first two weeks of a semester or move down during the first three weeks. Please contact the instructor for more details or if this is not applicable.

How does grading work?

Final scores (rounded up to the nearest whole number) are compared to the grading scale given in the syllabus to determine a final grade. Individual scores or grades will not be modified because they represent a student's progress in the class throughout the semester. If there is a mistake in scoring, please contact the instructor as soon as possible to get the error fixed.

Midterm grades do not have a score table so are based on the percentage of points completed at the time of midterm submission.

Note: I dislike the University's scale of "F" because I have never once felt that a student has "failed" a class. Instead, I prefer to think of this as a "not pass" where insufficient evidence has been demonstrated by a student to move on to the next level.

What if I need accommodations (like extra time on tests)?

Please let me of know ways I might be helpful when you notice possible suggestions. For individual accommodations, please contact the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

What else do I need to know?