Mathematics

Follow your passion for Math

Are you looking for a useful, challenging and practical major? Would you like an active, supportive community of faculty mentors to guide you in your studies?

The Mathematics program at Loras prepares students to argue rigorously, think abstractly and problem-solve creatively. These skills provide an edge in a wide variety of careers, as well as on graduate entrance exams. A study by the National Institute of Education found that on average, math majors scored higher than any other major on the LSAT and GMAT. If you’d like one of the top three “Majors That Pay You Back,” according to PayScale.com, Mathematics may be an excellent choice for you.

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MATHEMATICS AND COMPUTER INFORMATION TECHNOLOGY AWARDS AND SCHOLARSHIPS
AWARDS AND SCHOLARSHIPS

Mathematics and Computer Information Technology annually offer several awards and scholarships to students taking related courses. Some are available only to those majoring in Mathematics or Computer Information Technology while others are available to first-year students, regardless of their intended major. Winners are selected by Mathematics and Computer Information Technology faculty, and awards are presented at a ceremony each spring.

Computer Information Technology Awards and Scholarships

  • McKesson HBOC Scholarship — awarded since 1999.
    Two $1,000 scholarships are awarded annually. Candidates must be in their final year of study in Computer Science or Management Information Systems (MIS). Eligible candidates usually apply in April of each year and are required to submit a current transcript and an essay regarding their qualifications. A successful candidate will have excelled academically, been involved in extracurricular activities and demonstrated financial need. The recipients are chosen by representatives of McKesson HBOC along with Loras Accounting and Business, Mathematics and Computer Science faculty.

Past winners include: Sara Wieland, 2003; Deanna Ernzen, 2002; Angela Starkey (CS), 2001; Theodore Swanson (CS) and Curtis Kuhn (MIS), 2000; and Kevin Klemke and Erik Sterud, 1999.

  • Computer Information Technology Alumni Award — awarded since 1986.
    Candidates must be graduating seniors and nominated by a faculty member teaching a computer science-related course. Each candidate is asked to submit an essay detailing how they plan to use their experience in the future. The winner is selected by faculty vote. Recently, winners have garnered $100, a certificate and a nameplate engraved in their honor and displayed in Hennessy Hall.

Mathematics Awards and Scholarships

  • First-Year Mathematics Award — awarded since 1980.
    Recent winners have received $100 and a certificate in addition to the coveted handshake from the department chairperson. Candidates must be first-year students and nominated by a department faculty member. Each nominee is asked to submit a mathematical autobiography, and the winner(s) are chosen by department vote. Winners’ names are proudly displayed on nameplates near the main entrance of Hennessy Hall.
  • Droessler Scholarship — awarded since 1994.
    A scholarship in the amount of $2,000 is awarded annually from the endowment graciously provided by Dr. Earl Droessler, Professor Emeritus of the Department of Marine, Earth and Atmospheric Sciences at North Carolina State University. Dr. Droessler is a 1942 graduate of Loras College. A candidate for this scholarship must have either junior or senior standing, have declared a mathematics major and have a minimum 3.0 GPA in all courses. Strong candidates will have shown creativity and devotion to their study of mathematics and the liberal arts in general, and be involved in extracurricular activities. Candidates are nominated by department faculty members, and winners are selected by a vote of the department faculty.
  • Sullivan Applied Mathematics and Science Award — awarded since 2001.
    Recipients receive $500. The Sullivan award is intended to reward and provide further motivation for female majors in Mathematics, Computer Science, Physics or Engineering. Candidates for this annual award must maintain a 3.5 GPA and have demonstrated quality course selection in the pursuit of a liberal arts education.
  • Father Louis Ernsdorff Senior Math Award — awarded since 1980.
    Winners of the award receive $100, a certificate and a nameplate engraved in their honor and displayed in Hennessy Hall. Candidates for this award must be graduating seniors nominated by a faculty member in the department. The winner is then selected by a vote of the department faculty.

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LORAS COLLEGE MATH CLUB

Loras has an active Math Club which hosts a variety of events, including game nights, Sudoku contests, a Pi Day “Pie Your Professor” contest, and a high school math competition.

The Loras Math Club meets monthly and hosts several events throughout the year, including Sudoku contests, board game nights, Family Feud-style game shows, and the infamous “Pie Your Professor” contest on Pi Day. For the past several years, the club has helped sponsor student trips to undergraduate research conferences, traveling to Pi Mu Epsilon at St. Norbert College in the fall and the Midwest Undergraduate Mathematics Symposium at Simpson College in the spring.

The club also helps promote the Bi-State Math Colloquium, a series of informative talks by faculty, graduate students and undergrads from colleges and universities in Iowa and Wisconsin. In addition, math club members participate in a variety of math contests, including the Iowa Collegiate Math Contest, the Mathematical Competition in Modeling, the Iowa Mathematical Modeling Contest and the Putnam Exam.

Math Club also enjoys coming together with faculty members in the department to socialize and serve. Students in all math classes are invited to Tasty Tuesdays, a weekly evening of snacks, socializing and math homework help from professors. The club encourages alumni to return annually by reserving a spot at the Homecoming Tailgate. The club also participates in a variety of service projects. Last year, they helped run a Great Plains Math League high school math tournament at Loras.

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WHY MATH AT LORAS COLLEGE?

Conferences and Competitions, Bi-State Math Colloquium, Math Club, Faculty Support

Conferences and Competitions: Students can travel to conferences to meet new people and share their discoveries. Our math majors regularly present their work at the Pi Mu Epsilon Regional Undergraduate Math Conference in the fall and the Midwest Undergraduate Mathematics Symposium in the spring. Our students also compete in a variety of college-level regional and national math competitions, including the Iowa Collegiate Mathematics Competition and the Iowa Mathematical Modeling Competition.

Bi-State Math Colloquium: Students hear of developments in the field by staying on campus, too. Loras College is co-host of the weekly Bi-State Math Colloquium with UW-Platteville. Speakers for the colloquium series include professors, graduate students and undergrads from colleges and universities in the region presenting talks ranging from brand-new research to the ancient history of math.

Math Club: Loras has an active Math Club, which hosts a variety of events including game nights, Sudoku contests, a Pi Day “Pie Your Professor” Contest, and a high school math competition.

Faculty Support: Math students at Loras receive lots of support. In addition to regular office hours, the math faculty holds Math Lab in the library 12 hours a week. Faculty also host evening help sessions both on- and off-campus for homework and fellowship help.

What Are the Requirements?
Students interested in pursuing advanced study in mathematics or related fields can choose courses that will prepare them for graduate school.

Students who wish to use mathematics in industry or want to supplement majors in fields such as engineering, computer science, economics or chemistry can choose the courses that will aid them in other fields.

Students planning to teach high school mathematics can take those courses that are required for licensure to teach math, as well as other courses to prepare for teaching at the secondary level.

In addition to standard coursework, each major completes either a one-semester capstone class, in which students work in groups for a collaborative research experience, or a three-semester seminar sequence, in which students pursue individual undergraduate research projects with faculty advisors.

Are you looking for a useful, challenging, practical major? Would you like an active, supportive community of faculty mentors to guide you in your studies? If so, the Loras College mathematics major may be an excellent choice for you.

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LORAS MATH MAJORS PARTICIPATE IN NATIONAL PROGRAMS

Proposing a model of nonlinear ordinary differential equations and showed the existence of coexistence, recurrence, and cure steady states.

Katie Gonzales (’14) spent the summer of 2013 interning with the Women’s National Basketball Association’s Chicago Sky. Being a math and sport management double major, this internship allowed Katie to use skills she’s learned in both areas. After completing her internship, Katie used data from the Sky for her senior math project. She worked with Dr. Matt Rissler to calculate wins produced in the WNBA, based off models used in the NBA.

Patricia McCarthy (’15) (Highlands Ranch, Colorado) was chosen to participate in a Research Experience for Undergraduates (REU) at Winthrop University during summer 2014. REUs are highly selective national programs funded by the National Science Foundation. Tricia’s REU group worked with Dr. Kristen Abernathy in the use of the cancer stem cell hypothesis in the study of treatment of Glioblastoma Multiform by immunotherapy. Their project proposed a model of nonlinear ordinary differential equations and showed the existence of coexistence, recurrence, and cure steady states. Tricia and her team traveled to the Joint Mathematics Meetings in January to present their research.

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Student Learning Outcomes
Student Learning Outcomes – Mathematics
1. Students will demonstrate proficiency in oral mathematical communication
2. Students will demonstrate proficiency in written mathematical communication
3. Students will engage in the mathematical processes of creative problem solving, pattern recognition, and conjecture forming.
4. Students will reflect on their process of productive struggle in mathematics
5. Students will produce and evaluate the quality of mathematical arguments
6. Students will apply analytical and procedural skills in a variety of contexts
7. Students will synthesize various mathematical strategies to tackle authentic problems in novel settings
Major Requirements

MATHEMATICS
Division of Mathematics, Engineering & Computer Science
Robert S. Keller, Ph.D., Chair
robert.keller@loras.edu
563.588.7105

The mathematics major allows students to tailor their major to their goals and careers after graduation.

Requirements for the major in Mathematics (B.S.):
A minimum grade of a C (2.000) received in each of Reqs 1 through 5, and average of a C (2.000) in all courses applied to the student’s major is required. All majors must also take L.MAT-490, the capstone experience for mathematics majors in which students produce a portfolio linking experiences obtained in their major with the general education curriculum (the exception for students receiving licensure at the secondary level from the Education division is that they will take L.EDU-490 in place of L.MAT-490). Requirements #1-6 identified below comprise the mathematics core.

Req Course Cr’s
1 L.MAT-150: Calc of One Variable I 4
2 L.MAT-160: Calc of One Variable II 4
3 L.MAT-230: Discrete Mathematics 3
4 L.MAT-250: Linear Algebra 3
5 L.MAT-260: Analytic Geometry and Calculus III 4
6 L.CIT-115:   Introduction to Programming 4
Select one from Req 7
7 L.CIT-225: Data Structures & Algorithms 4
7 L.PHY-223: Physics Scientist/Engineers I 5
7 L.EDU-353: Special Sec Methods: Mathematics 3
Select either all three of Req 8a, or Req 8b
8a L.MAT-390: Seminar 1
8a L.MAT-390: Seminar 1
8a L.MAT-390: Seminar 1
8b L.MAT-391: Guided Research 3
Select four from Req 9a-9b; of those, at least one from 9b
9a L.MAT-220: Introduction to Probability & Statistics 3
9a L.MAT-310: Ordinary Differential Equations 3
9a L.MAT-370: Numerical Analysis 3
9a L.MAT-380: Modern Geometry 3
9a L.MAT-395: Topics 3
9b L.MAT-450: Modern Algebra 3
9b L.MAT-460: Real Analysis 3
9b L.MAT-495: Topics 3
10 L.MAT-490: Mathematics Portfolio 1
41 to 43 total required credits

Requirements for the minor in Mathematics:
A minimum grade of C- is required in each course for the minor.

Req Course Cr’s
1 L.MAT-150: Calc of One Variable I 4
2 L.MAT-160: Calculus on One Variable II 4
3 L.MAT-220+: Additional L.MAT course 3 to 4
4 L.MAT-220+: Additional L.MAT course 3 to 4
5 L.MAT-220+: Additional L.MAT course 3
17 to 18 total required credits
Course Descriptions

L.MAT-091: Intermediate Algebra

This course is designed to prepare the student for college-level (100-level) coursework in mathematics. The course covers arithmetic, pre-algebra, and elementary and intermediate algebra, including linear equations and linear functions and applications, and exponents. 4 credits.

L.MAT-110:  Math for K-8 Teachers I

This course begins to develop the solid foundation in K-8 mathematics needed by future elementary and middle school teachers. The focus of this course is on Numbers and Operations. In addition, this course will introduce students to professional recommendations and state requirements for mathematics instruction and provide students with a global perspective on mathematics achievement. This course does not fulfill mathematical modeling general education requirements. 4 credits.

L.MAT-111:  Math for K-8 Teachers II

This course provides further instruction on K-8 mathematics for prospective elementary and middle school teachers. L.MAT-111 focuses on the content domains of Geometry, Measurement, Probability, and Algebraic Thinking. The course topics are taught using teaching techniques appropriate for elementary and middle school, including guided discovery and other student-centered approaches.

Prerequisite: L.MAT-110. 4 credits.

L.MAT-113: College Algebra-FM

Advanced work in algebra, functions and graphing in the context of mathematical models. Topics include linear, polynomial, exponential and logarithmic functions and regression. Prerequisite: a grade of C- or better in L.MAT-091 or placement into L.MAT 113. May not be taken for credit if a grade of C or higher was achieved in MAT-117 or a higher level mathematics course. 3 credits.

L.MAT-115: Statistics-FM

Basic statistical concepts and methods. Descriptive statistics and probability, distribution and sampling theory, hypothesis testing and analysis of variance, correlation and regression. Prerequisite: a grade of C- or better in L.MAT-091 or placement into L.MAT 115. 4 credits.

L.MAT-117: Pre-Calculus-FM

This course provides a one semester preparation for calculus while presenting an introduction to mathematical modeling. Topics include: linear, quadratic, exponential, and trigonometric models. Prerequisite:  a C- or better in L.MAT-113 or placement into L.MAT 117. 4 credits.

L.MAT-150: Calculus of One Variable I-FM

A study of the basic concepts and techniques of analytic geometry, differential and integral calculus of functions of one variable, and applications to calculus-based models. Prerequisite: Demonstrated competency in L.MAT-113 and 117 or equivalent or placement into L.MAT 150. 4 credits.

L.MAT-160: Calculus of One Variable II

Further study of the integral calculus of functions of one variable and an introduction to sequences, series, and differential equations. Prerequisite: L.MAT-150 or equivalent. 4 credits.

L.MAT-220: Introduction to Probability & Statistics

A study of the fundamental techniques used in descriptive statistics as applied to real-world data and the processes associated with the design and analysis of experiments; application of theories from calculus to the construction of cumulative distributions for continuous random variables and computation of associated probabilities, expected values and variances. Prerequisites: L.MAT-150, and one of L.MAT-160, L.CIT-115, or L.EGR-116. 3 credits.

L.MAT-230: Discrete Mathematics

This course introduces the ideas and methods of logic and proofs. Topics include: set theory, logic, functions, proof types and elementary number theory. Prerequisite: L.MAT ­150 and one of L.MAT-160, L.CIT-115, or L.EGR-116 (these last three can be taken as a co-requisite). 3 credits.

L.MAT-250: Linear Algebra

A course which introduces abstract vector spaces, matrices and linear transformations. Prerequisite: L.MAT-150 and one of L.MAT-160, L.CIT-115, or L.EGR-116 (these last three can be taken as co-requisite).  3 credits.

L.MAT-260: Analytic Geometry & Calculus III

A study of partial differentiation and multiple integration, elementary vector analysis and applications of these concepts. Prerequisite: L.MAT-160 or placement into L.MAT-260. 4 credits.

L.MAT-310: Ordinary Differential Equations

Theory, solution and applications of ordinary differential equations including Laplace transform methods. Prerequisite: L.MAT-160. 3 credits.

L.MAT-370: Numerical Analysis

A study of some of the standard numerical algorithms used to solve real-world problems arising in engineering and the sciences, and use of a computer to implement these algorithms; pitfalls in computation, error analysis, solving linear systems, interpolation and approximation. Prerequisites: L.MAT-160 and L.CIT-115. 3 credits.

L.MAT-380: Modern Geometry

Both Euclidean and non-Euclidean geometries are studied from an axiomatic viewpoint. Traditional high school geometry concepts are presented in a rigorous fashion so as to expand one’s depth of understanding of traditional geometry. Prerequisite: L.MAT-230 or permission of the instructor. 3 credits.

L.MAT-390: Mathematics Seminar

A course where students experience and learn mathematics beyond that contained in usual coursework. Participants carry out research in an area of mathematics of interest to them with a faculty mentor. Each student gives at least one presentation on their topic and make definite progress toward the completion of the senior paper and presentation. Prerequisite: L.MAT-260, and 230; L.MAT-250 can be taken as a co-requisite. 1 credit (may be repeated).

L.MAT-391: Guided Research

A course where students experience and learn mathematics beyond that contained in usual coursework. Participants carry out research in an area of mathematics in a small group. Groups will give presentations and submit a final artifact. Prerequisite: L.MAT-230, L.MAT-250, and L.MAT-260. 3 credits.

L.MAT-450: Modern Algebra

A course which covers basic ideas on groups, rings, integral domains, fields, and polynomials over a field. Prerequisite: L.MAT- 230, and L.MAT-250 can be taken as a pre-requisite or co-requisite, or permission of instructor. 3 credits.

L.MAT-460: Real Analysis

Further work in calculus, including the properties of the real number system, limits and continuity, differentiation and integration, sequences and series. Prerequisite: L.MAT-160 or 170, and L.MAT-230 (or permission of instructor); L.MAT-250 can be taken as a pre-requisite or co-requisite. 3 credits.

L.MAT-490: Math Portfolio-PJ

Students will assemble a portfolio that provides evidence of appreciable growth in their understanding of mathematics, and reflect on the relevance of the Loras College dispositions and lifelong learning skills to their development in the major and as a person. This course satisfies the general education portfolio requirement. Prerequisite: Declared Mathematics major, completion of three of the five advanced general education courses, L.MAT-230, 250, and 260, L.MAT-391 or at least two semesters of L.MAT-390. 1 credit.

L.MAT-495: Topics in Mathematics

Selected topics of current interest to students. Prerequisite: Permission of instructor. Credits arranged.

RELATED COURSES: Computing & Information Technology, Engineering

CAREER OPPORTUNITIES

After receiving your degree from Loras, your career could take off into one of these fields:

• Math Teacher
• Biologist
• Software Engineer
• Computer Systems Analyst
• Business
• Accountant
• Economist
• Computer Programmer
• Meteorologist

Questions? Contact Us!

Robert Keller, Ph.D.
Division of Mathematics, Engineering, & Computer Science Chair
Professor of Mathematics
563.588.7015 | Robert.Keller@loras.edu

Curriculum Vitae

Robert Keller is Associate Professor of Mathematics at Loras College and Chair of the Division of Mathematics, Engineering, and Computer Science. Rob has taught at Loras since earning his Ph.D. in Mathematics in 1999 from the University of North Carolina, Chapel Hill. From 2000-2004 he taught 5th- and 6th-grade Dubuque public school students part time through the Talented and Gifted program. For the past decade, Rob has delivered professional development in mathematics, and more recently in STEM education, for practicing K-12 teachers. These have included workshops for high school teachers transitioning to a standards-based beginning algebra series, and more than six years as a lead organizer and presenter for the Loras College Lesson Study Project. Funded by several large grants, this project was a successful partnership involving the Mississippi Bend and Keystone Area Education Agencies and educators from Loras College that ultimately served hundreds of teachers throughout eastern Iowa.

Currently, he is co-director of a three-year Title IIA-funded project which seeks to build capacity to deliver integrated middle school science and mathematics content. More than 50 middle school teachers from six school districts are currently involved in this unique project. Rob has also been active in the education and formation of future K-12 teachers. He co-directed the development of a two-course sequence in mathematics content for K-8 teachers at Loras College (funded by a Preparing Mathematicians to Educate Teachers grant awarded through the NSF and Mathematics Association of America), which he now regularly teaches. He has collaborated with Bridgette Stevens (formerly at the University of Northern Iowa) on testing methods to promote the integration of reflective practices in mathematics courses for elementary teachers, work that was funded by an inter-institutional grant from UNI. In addition, from 2002-2004 Rob led efforts with Joyce Becker of Luther College and Catherine Miller of the University of Northern Iowa to update Iowa state requirements for pre-service Secondary Math Education majors (with funding by grants from the Regents Academy and UNI).

Susan Crook, Ph.D.
Associate Professor of Mathematics
563.588.7794 | Susan.Crook@loras.edu

Susan Crook earned her Ph.D. from North Carolina State University in 2013. At NCSU she worked in Numerical Analysis focusing on curve matching, which has real-world applications in object recognition and assembly. Since coming to Loras, Dr. Crook’s research has focused more on happy numbers (with a research group supported by the American Institute of Mathematics). She is interested in inquiry-based learning, both in the classroom and as a research topic. While she enjoys research, her real passion is teaching.

At Loras, Dr. Crook has had the pleasure of teaching a variety of math courses and engaging with students across many majors. She loves getting students actively involved in playing with mathematics so that they can enjoy the “ah ha!” moments that mathematicians do. In her free time, Dr. Crook enjoys cooking and baking, traveling the world, discovering new musicians, and reading while cuddled up with her two cats, Penny and Nona.

Jacob Heidenreich, Ph.D.
Associate Professor of Mathematics
563.588.7793 | Jacob.Heidenreich@loras.edu

Curriculum Vitae

Prof. Heidenreich’s training is in mathematics and philosophy, centering on the field of Mathematical Logic. He has a strong interest in the historical development of mathematics, as well as the philosophical issues that have arisen during that development. In the past, he has worked on developing undergraduate research and the senior experience in the math program at Loras College. He developed the system by which math majors engaged in undergraduate research and present that research to their peers and professors. He also was responsible for beginning a tradition of student attendance and presentation at undergraduate conferences in mathematics. Recently, his interest is in the use of games in the classroom to enable deep student learning. He studies good game design, and how those design principles can be used to design various assignments and activities. He also develops games for use as teaching tools in the classroom.

Karen Heidenreich
Instructor of Mathematics
563.588.7971 | karen.heidenreich@loras.edu

Dr. Karen Heidenreich earned her Ph.D. in mathematics from the University of Notre Dame in August 2000, where she studied highest weight representations of infinite dimensional Lie algebras.  Before coming to Loras with her husband Jacob, she taught for six years at Grand Valley State University in Allendale, MI.  Currently Dr. Heidenreich teaches classes both on the Loras campus and at the local high schools.  She also serves as a member of the STEM committee for the Northeast Iowa Council of the Boy Scouts of America, where she works to develop exploratory STEM activities for elementary age children.  In her spare time she enjoys reading, sewing, playing board games, and hanging out with her kids.

Angela Kohlhaas, Ph.D.
Associate Professor of Mathematics
563.588.7152 | Angela.Kohlhaas@loras.edu

Curriculum Vitae

Dr. Kohlhaas received her PhD in mathematics in 2010 from the University of Notre Dame, where she studied commutative algebra. She enjoys finding ways of visualizing abstract algebraic and geometric concepts, and her students spend an inordinate amount of time playing with Play-Doh as a result. She also loves engaging students in undergraduate research projects, with topics ranging from the mathematics of origami to symmetries of Sudoku. She recently developed a January term course investigating the mathematics of musical compositions and perspective art which she is excited to be teaching in January 2015. Outside of mathematics, Professor Kohlhaas can often be found playing Ultimate Frisbee, at the piano, or cooking spicy food.

Matthew Rissler, Ph.D.
Associate Professor of Mathematics
563.588.7792 | Matthew.Rissler@loras.edu

Dr. Rissler is originally from Virginia, but spent nine years in Indiana at Goshen College and the University of Notre Dame earning degrees in Mathematics, Physics, and Applied Math. Since 2008 he has been at Loras College teaching all of these and Statistics. His classes tend to involve using laptops to complete activities and modeling projects. Rissler’s research interests lie in the areas of agent-based modeling, statistics and utilizing computers in teaching Mathematics. Current and recent senior projects he has advised include simulating battles between orcs and elves (if you like LotR, or humans and zombies if you don’t), statistical modeling of production by players in the WNBA, and looking at streaks in baseball at the college level.