WHAT WE ARE
The Lindenwood Honors Sequence in Mathematics is a challenging series of courses designed for a small and motivated group of incoming math majors. The goal of the sequence is to provide a rigorous foundation in mathematics that will prepare students to pursue graduate study and careers in research and academia. Students selected to participate in the sequence will embark on an ambitious and intensive program of study for their first two years, and then work closely with faculty on research and reading projects in more advanced areas of mathematics that align with the student’s interests. In addition, Honors Sequence participants will contribute to the academic culture of the department by giving talks, mentoring younger students, holding review sessions, and running math outreach programs for the local community.
WHAT TO EXPECT
The first course in the sequence - Introduction to Advanced Mathematics - lays the logical foundations for mathematical proofwriting and reasoning. Each course thereafter will build on this foundation while developing a particular mathematical theory in depth. Honors Sequence candidates should be prepared to devote a significant amount of time outside of class to reviewing course material and thinking through assigned problems. We have found that students who continue their mathematical studies during the summer months stand to benefit the most from the Honors Sequence, although it is not required.
While the Honors Sequence will be very demanding, the Lindenwood math faculty are eager to help as much as possible along the way. We believe the considerable time and effort expended by our Honors Sequence scholars will be commensurate to the educational payout. Through their repeated exposure and engagement with beautiful and important mathematical ideas, Honors Sequence students will become disciplined and sophisticated thinkers. Moreover, the Honors Sequence will encourage extensive collaboration among its participants; we envision the students in the program becoming a tightly-knit community of scholars who teach, learn from, and rely on one another.
WHO SHOULD APPLY
There are no formal prerequisites needed to apply to the Honors Sequence, and we will give careful consideration to any applicant who is interested in seriously pursuing mathematics. While natural mathematical aptitude may be an asset in the beginning, we have found that a more reliable predictor of success in the Honors Sequence is a student’s patience and tenacity when faced with difficult problems. In addition, successful candidates are honest, humble, generous, and willing to work cooperatively with other students in the program. If you have any questions or concerns about the program, please direct them to Professor Nikhil Gupta.
To help you determine whether the Honors Sequence might be a good academic fit, we invite you to consider the collection of problems below. You may find these problems to be quite different from problems you’ve come across in your high school math classes; as such, do not be discouraged if there are problems that you find challenging! As you work through the problems, please keep the following in mind:
- It is a significant accomplishment to solve just one of these problems, and we certainly do not expect full solutions to every problem. It is preferable to think deeply about a few problems that grab your attention, rather than thinking superficially about all the problems.
- Time spent thinking about a problem is worthwhile, even if you feel like you haven’t made much progress towards a solution. We are interested to see how you think about a difficult problem. Please help us do this by documenting your thinking in an organized way. Record all observations and progress you make (even if its only partial progress) towards a solution. If you do manage to solve a problem fully, excellent! Please provide a detailed explanation of your solution.
- There is no limit to how long you can work on the problems. We hope you find at least one problem interesting enough to think about in a careful and sustained way.
- Please be honest about the work you submit; it should be an accurate reflection of your own thinking. You may consult general references to help you with a problem, but we don’t expect you to do so. If you do consult a reference, please make sure to cite it.
Please submit solutions to the application problems you’ve thought about. After you’ve finished thinking through the problems, please also respond to the following questions:
- Which of the application problems captured your interest the most? Why?
- Briefly describe your educational background in mathematics. Feel free to also comment on the following: What makes you interested in pursuing mathematics in college? Why are you interested in the Honors Sequence in particular? What mathematical topics would you like to learn about?
Scan or take a photo of your problem solutions as well as the responses to the questions above, and send them to Professor Nikhil Gupta by July 15, 2020. Students that are selected for the Honors Sequence will be notified via email by August 15, 2020.
Good luck! We look forward to seeing what you come up with.