- Department of Mathematics and Statistics
- Outreach
- Summer Mathematics Institute

**
Department of Mathematicsand Statistics
**

Mathematics and Science Center, Room 368

146 Library Drive

Rochester,
MI
48309-4479

**(location map)**

phone: (248) 370-3430

fax: (248) 370-4184

**Hours:**

Monday–Friday: 8:00–11:59 a.m. and 1:00–5:00 p.m.

**Summer Mathematics Institute**

Department of Mathematics and Statistics

Oakland University

Rochester, MI 48309-4485

Phone: (248) 370-3430

Fax: (248) 370-4184**Professor Eddie Cheng, Director**

e-mail: echeng@oakland.edu

Phone: (248) 370-4024

# Summer Mathematics Institute

**Summer Mathematics Institute**

For Bright and Gifted Pre-College Students

For Bright and Gifted Pre-College Students

The Summer Mathematics Institute is a free opportunity for bright and gifted pre-college students to interact with university faculty and each other, to take some challenging math classes that earn college credit, and have fun in an academic atmosphere. The Institute runs approximately from late June through the first week of August each summer. Students are encouraged to apply early (before the deadline of mid-May). If you are interested in applying, you may request an application by sending an email to echeng@oakland.edu.

The Institute Director

**Dr. Eddie Cheng**is Distinguished Professor of Mathematics in the Department of Mathematics and Statistics at Oakland University. He joined the faculty of Oakland University as an assistant professor in 1997, promoted to associate professor in 2001, promoted to professor in 2007 and given the rank of distinguished professor in 2011; in addition, he served as Chair of the department from 2010 to 2013.

Professor Cheng graduated with a B.Sc. (Hons.) from Memorial University of Newfoundland (Canada) in 1988. During the summer of 1988, he worked as a research assistant in the Department of National Defence in British Columbia. For his graduate studies, he earned his M.Math. in 1990 and Ph.D. in Combinatorics and Optimization from the University of Waterloo (Canada) in 1995. From 1995 to 1997, he was a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellow and part-time lecturer in the George R. Brown School of Engineering at Rice University. He was a member of the examination committee of the Michigan Mathematics Prize Competition (MMPC) from 2001 to 2005, from 2008 to 2012 and from 2013-2017. He also served as the Director of MMPC from 2005 to 2008. MMPC is a state-wide competition given every year to thousands of high school students in Michigan.

He is also a member of the editorial board and an associate editor of the journal

*Networks*.

*Networks*publishes material on the modeling of problems using networks, the analysis of network problems, the design of computationally efficient network algorithms, and innovative case studies of successful network applications. In addition, he is a managing editor of

*Journal of Interconnection Networks*. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks.

His research interests include combinatorial optimization, integer programming and network analysis. He has authored and coauthored about 180 research papers. Professor Cheng has directed a number of high school students for projects that advanced to semifinals and beyond in national competitions such as Siemens Competitions and the Intel Science Talent Search. Many of these projects resulted in publications in refereed journals. He is the recipient of the 2007 Mathematical Association of America (Michigan Section) Distinguished Teaching Award and a recipient of the 2009 Professor of the Year Award from the Presidents Council, State Universities of Michigan.

The Institute Past Directors

**Dr. Marc Lipman**served as the director from 1997 to 2002. During this time he was Professor and Chair of the Department of Mathematics and Statistics at Oakland University. He graduated from Lake Forest College in 1971 with a double major in Mathematics and Physics. He earned his Ph.D. from Dartmouth College in 1976. From 1976 to 1989, he was a faculty member at Indiana University-Purdue University Fort Wayne. During this time, he spent 1980–1981 at the Naval Research Laboratory in Washington, D.C.. From 1989 to 1997, he was the scientific officer in charge of the four million dollar Discrete Mathematics program at the Office of Naval Research. His research interests include interconnection networks, communication network topology and sphere-of-influence graphs. He has authored and coauthored over 50 research papers. Among other things, he's taught at STAR, the residential summer camp for bright and gifted students at Purdue University. He left Oakland University to be the Dean of the School of Arts and Sciences at IUPU Fort Wayne.

**was the first director (1996–1997) of the institute. Dr. McKay was the first professor in the department in 1959 and served as the chair of the department for many years through the 1990's. He retired in 1997.**

Dr. James H. McKay

Dr. James H. McKay

Courses Offered

1996 | APM 263 Discrete Mathematics | MTH 372 Number Theory |

1997 | STA 226 Applied Statistics | MTH 475 Abstract Algebra |

1998 | MTH 256,266 Linear Algebra with Laboratory | STA 405 Probability |

1999 | APM 405 Linear Programming | MTH 302 Introduction to Advanced Mathematical Thinking |

2000 | APM 405 Combinatorics: Enumeration | STA 226 Applied Statistics |

2001 | APM 405 Introduction to Graph Theory | MTH 461 General Topology |

2002 | MTH 256,266 Linear Algebra with Laboratory | MTH 372 Number Theory with Cryptography |

2003 | MOR 342 Introduction to Operations Research | MTH 302 Introduction to Advanced Mathematical Thinking |

2004 | APM 405 Combinatorics: Enumeration | MTH 361 Geometric Structures |

2005 | APM 405 Introduction to Graph Theory | STA 226 Applied Statistics |

2006 | MTH 275 Linear Algebra | MTH 372 Number Theory with Cryptography |

2007 | MOR 454 Linear and Integer Optimization | MTH 302 Introduction to Advanced Mathematical Thinking |

2008 | APM 405 Combinatorics: Enumeration | MTH 462 Geometric Structures |

2009 | APM 405 Introduction to Graph Theory | APM 367 Design and Analysis of Algorithms |

2010 | MTH 275 Linear Algebra | MTH 472 Number Theory with Cryptography |

2011 | MOR 454 Linear and Integer Optimization | MTH 302 Introduction to Advanced Mathematical Thinking |

2012 | APM 405 Combinatorics: Enumeration | MTH 462 Geometric Structures |

2013 | APM 405 Introduction to Graph Theory | APM 367 Design and Analysis of Algorithms |

2014 | MTH 275 Linear Algebra | MTH 472 Number Theory with Cryptography |

2015 | MOR 454 Linear and Integer Optimization | MTH 302 Introduction to Advanced Mathematical Thinking |

2016 | APM 405 Combinatorics: Enumeration | APM 381 Theory of Computation |

2017 | APM 405 Introduction to Graph Theory | APM 367 Design and Analysis of Algorithms |

2018 | MTH 275 Linear Algebra | MTH 472 Number Theory with Cryptography |

2019 Summer Mathematics

Institute

Institute

**2019 Summer Mathematics Institute**

**Program Announcement**

July 8 – August 16, 2019

The Institute provides an opportunity for bright and gifted pre-college students to interact with university faculty and each other, to take some challenging math classes that earn college credit, and have fun in an academic atmosphere.

Students take two 4-credit courses in mathematics or statistics taught by full-time doctoral-holding faculty.

The Summer Mathematics Institute at Oakland University is free to all participants.

The Summer Mathematics Institute at Oakland University is a day camp.

Completed applications will be given full consideration if received by May 15, 2019. (Application material will be available in March.)

Download the sample problem set, to include with your application.

Please contact Professor Eddie Cheng echeng@oakland.edu for application.

Professor Cheng graduated with a B.Sc. (Hons.) from Memorial University of Newfoundland (Canada) in 1988. During the summer of 1988, he worked as a research assistant in the Department of National Defence in British Columbia. For his graduate studies, he earned his M.Math. in 1990 and Ph.D. in Combinatorics and Optimization from the University of Waterloo (Canada) in 1995. From 1995 to 1997, he was a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellow and part-time lecturer in the George R. Brown School of Engineering at Rice University. He was a member of the examination committee of the Michigan Mathematics Prize Competition (MMPC) from 2001 to 2005, from 2008 to 2012 and from 2013-2017. He also served as the Director of MMPC from 2005 to 2008. MMPC is a state-wide competition given every year to thousands of high school students in Michigan.

He is also a member of the editorial board and an associate editor of the journal

His research interests include combinatorial optimization, integer programming and network analysis. He has authored and coauthored about 180 research papers. Professor Cheng has directed a number of high school students for projects that advanced to semifinals and beyond in national competitions such as Siemens Competitions and the Intel Science Talent Search. Many of these projects resulted in publications in refereed journals. He is the recipient of the 2007 Mathematical Association of America (Michigan Section) Distinguished Teaching Award and a recipient of the 2009 Professor of the Year Award from the Presidents Council, State Universities of Michigan.

Activities are scheduled Monday through Thursday from 8:30 a.m. - 3:30 p.m. and Friday from 8:30 a.m. - 1:00 p.m. Students will attend special sections of two regular Oakland University courses that generate regular university credit. Generally, each class will meet every day. When not in class, the students will be in small groups under the direct supervision of counselors. Small group sessions will include opportunities to do homework, problem solving, computer instruction and practice, and other mathematical recreations.

Lunch will be provided (FREE) every day.

The Summer Mathematics Institute at Oakland University closes with a banquet. Parents, students' high-school mathematics teachers, and their high-school principals will be invited. The program will include the presentation of Certificates of Completion to the students. We will also provide signed testimony regarding the college credit courses taken during the Institute.

The Distinguished Colloquium Speaker: TBA.

The Institute Director and Instructor

Dr. Eddie Cheng is Distinguished Professor of Mathematics in the Department of Mathematics and Statistics at Oakland University. He joined the faculty of Oakland University as an assistant professor in 1997, promoted to associate professor in 2001, promoted to professor in 2007 and given the rank of distinguished professor in 2011; in addition, he served as Chair of the department from 2010 to 2013.Professor Cheng graduated with a B.Sc. (Hons.) from Memorial University of Newfoundland (Canada) in 1988. During the summer of 1988, he worked as a research assistant in the Department of National Defence in British Columbia. For his graduate studies, he earned his M.Math. in 1990 and Ph.D. in Combinatorics and Optimization from the University of Waterloo (Canada) in 1995. From 1995 to 1997, he was a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellow and part-time lecturer in the George R. Brown School of Engineering at Rice University. He was a member of the examination committee of the Michigan Mathematics Prize Competition (MMPC) from 2001 to 2005, from 2008 to 2012 and from 2013-2017. He also served as the Director of MMPC from 2005 to 2008. MMPC is a state-wide competition given every year to thousands of high school students in Michigan.

He is also a member of the editorial board and an associate editor of the journal

*Networks*.

*Networks*publishes material on the modeling of problems using networks, the analysis of network problems, the design of computationally efficient network algorithms, and innovative case studies of successful network applications. In addition, he is a managing editor of

*Journal of Interconnection Networks*. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks.

His research interests include combinatorial optimization, integer programming and network analysis. He has authored and coauthored about 180 research papers. Professor Cheng has directed a number of high school students for projects that advanced to semifinals and beyond in national competitions such as Siemens Competitions and the Intel Science Talent Search. Many of these projects resulted in publications in refereed journals. He is the recipient of the 2007 Mathematical Association of America (Michigan Section) Distinguished Teaching Award and a recipient of the 2009 Professor of the Year Award from the Presidents Council, State Universities of Michigan.

The Institute Instructor

Dr. László Lipták is Chair of the Department of Mathematics and Statistics at Oakland University. He joined the faculty of Oakland University in 2003, promoted to associate professor in 2007 and promoted to professor in 2013. He participated in mathematical competitions starting from grade 3, and represented his native country, Hungary, in two of the International Mathematical Olympiads, in 1986 (Warsaw, Poland) and 1987 (Havana, Cuba), receiving silver and bronze medals, respectively. He graduated with a B.S. from the University of Szeged, Hungary with honors in 1993, and received his Ph.D. in mathematics from Yale University in 1999. He was a Postdoctoral Fellow first at the Fields Institute in Toronto, Canada during 1999-2000, then at the University of Waterloo, Canada during 2000-2003. His research interests include combinatorial optimization, lifting-projecting methods, the stable set polytope, and interconnection networks. He has authored and coauthored about 60 research papers.Courses

**MOR 4554 - Linear and Integer Optimization, Dr. Eddie Cheng**

Topics include linear and integer programming models, simplex method, complementary slackness, duality, sensitivity analysis, interior point methods systems of alternatives and branch-price-cut.**MTH 3002 - Introduction to Advanced Mathematical Thinking, Dr. Laszlo Liptak**

The propositional and predicate calculus, set theory, methods of mathematical proof, inductive and recursive thinking, relations and functions, infinity. Emphasis is on rigorous proofs of mathematical statements.

Schedule

The 2019 Summer Mathematics Institute at Oakland University meets for for six weeks.Activities are scheduled Monday through Thursday from 8:30 a.m. - 3:30 p.m. and Friday from 8:30 a.m. - 1:00 p.m. Students will attend special sections of two regular Oakland University courses that generate regular university credit. Generally, each class will meet every day. When not in class, the students will be in small groups under the direct supervision of counselors. Small group sessions will include opportunities to do homework, problem solving, computer instruction and practice, and other mathematical recreations.

Lunch will be provided (FREE) every day.

The Summer Mathematics Institute at Oakland University closes with a banquet. Parents, students' high-school mathematics teachers, and their high-school principals will be invited. The program will include the presentation of Certificates of Completion to the students. We will also provide signed testimony regarding the college credit courses taken during the Institute.

2018 Summer Mathematics

Institute

Institute

**2018 Summer Mathematics Institute**

**Program Announcement**

July 9 – August 17, 2018

The Institute provides an opportunity for bright and gifted pre-college students to interact with university faculty and each other, to take some challenging math classes that earn college credit, and have fun in an academic atmosphere.

Students take two 4-credit courses in mathematics or statistics taught by full-time doctoral-holding faculty.

The Summer Mathematics Institute at Oakland University is free to all participants.

The Summer Mathematics Institute at Oakland University is a day camp.

Completed applications will be given full consideration if received by May 15, 2018.

Download the sample problem set, to include with your application.

Brochure in pdf format. Flyer in pdf format.

The Distinguished Colloquium Speaker: David Jao (University of Waterloo).

The Institute Director and Instructor

Dr. Eddie Cheng is Distinguished Professor of Mathematics in the Department of Mathematics and Statistics at Oakland University. He joined the faculty of Oakland University as an assistant professor in 1997, promoted to associate professor in 2001, promoted to professor in 2007 and given the rank of distinguished professor in 2011; in addition, he served as Chair of the department from 2010 to 2013.Professor Cheng graduated with a B.Sc. (Hons.) from Memorial University of Newfoundland (Canada) in 1988. During the summer of 1988, he worked as a research assistant in the Department of National Defence in British Columbia. For his graduate studies, he earned his M.Math. in 1990 and Ph.D. in Combinatorics and Optimization from the University of Waterloo (Canada) in 1995. From 1995 to 1997, he was a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellow and part-time lecturer in the George R. Brown School of Engineering at Rice University. He is currently a member of the examination committee of the Michigan Mathematics Prize Competition (MMPC), a position he held from 2001 to 2005 and from 2008 to 2012. He also served as the Director of MMPC from 2005 to 2008. MMPC is a state-wide competition given every year to thousands of high school students in Michigan.

He is also a member of the editorial board and an associate editor of the journal

*Networks*. Networks publishes material on the modelling of problems using networks, the analysis of network problems, the design of computationally efficient network algorithms, and innovative case studies of successful network applications. In addition, he is an editor of

*Journal of Interconnection Networks*. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks.

His research interests include combinatorial optimization, integer programming and network analysis. He has authored and coauthored about 160 research papers. Professor Cheng has directed a number of high school students for projects that advanced to semifinals and beyond in national competitions such as Siemens Competitions and the Intel Science Talent Search. Many of these projects resulted in publications in refereed journals. He is the recipient of the 2007 Mathematical Association of America (Michigan Section) Distinguished Teaching Award and a recipient of the 2009 Professor of the Year Award from the Presidents Council, State Universities of Michigan.

The Institute Instructor

Dr. László Lipták is Chair of the Department of Mathematics and Statistics at Oakland University. He joined the faculty of Oakland University in 2003, promoted to associate professor in 2007 and promoted to professor in 2013. He participated in mathematical competitions starting from grade 3, and represented his native country, Hungary, in two of the International Mathematical Olympiads, in 1986 (Warsaw, Poland) and 1987 (Havana, Cuba), receiving silver and bronze medals, respectively. He graduated with a B.S. from the University of Szeged, Hungary with honors in 1993, and received his Ph.D. in mathematics from Yale University in 1999. He was a Postdoctoral Fellow first at the Fields Institute in Toronto, Canada during 1999-2000, then at the University of Waterloo, Canada during 2000-2003. His research interests include combinatorial optimization, lifting-projecting methods, the stable set polytope, and interconnection networks. He has authored and coauthored about 60 research papers.

Courses

**MTH 4772 Number Theory with Cryptography, Dr. Eddie Cheng**

Structure of the integers, prime factorization, congruences, multiplicative functions, primitive roots and quadratic reciprocity, and selected applications including cryptography.**MTH 2775 Linear Algebra, Dr. Laszlo Liptak**

Study of general vector spaces, linear systems of equations, linear transformations and compositions, Eigenvalues, eigenvectors, diagonalization, modeling and orthogonality. Provides a transition to formal mathematics..

Schedule

The 2018 Summer Mathematics Institute at Oakland University meets for for six weeks.Activites are scheduled Monday through Thursday from 8:30 a.m. - 3:30 p.m. and Friday from 8:30 a.m. - 1:00 p.m. Students will attend special sections of two regular Oakland University courses that generate regular university credit. Generally, each class will meet every day. When not in class, the students will be in small groups under the direct supervision of counselors. Small group sessions will include opportunities to do homework, problem solving, computer instruction and practice, and other mathematical recreations.

Lunch will be provided (FREE) every day.

The Summer Mathematics Institute at Oakland University closes with a banquet. Parents, students' high-school mathematics teachers, and their high-school principals will be invited. The program will include the presentation of Certificates of Completion to the students. We will also provide signed testimony regarding the college credit courses taken during the Institute.