# Mathematics Curriculum

Mathematics includes an introduction to the principle branches of mathematics: calculus, algebra, probability, statistics, and analysis with emphasis on application of mathematics to the sciences and social sciences. The teacher certification program offers certification in secondary mathematics teaching. Students interested in this program should see the Certification Coordinator in the Education program for specific requirements.

# Program Requirements

## + Major Requirements (B.A. Degree)

## 42 credits, including: |
||

IND350 | Scientific Research Methods
This course serves as an introduction to research literature and research methodology in the sciences. Students prepare a research proposal including literature review, experimental design and methods, budget, timetable, and bibliography. Other topics include professional presentation techniques and research ethics. The student's major department must approve proposals prior to the Tutorial. Prerequisite(s): Junior status and completion of at least two courses at the 200-level or above in the major, or permission of the instructor. | 2 |

MTH110 | Elementary Statistics
Topics include statistical measures and distributions, decision making under uncertainty, application of probability to statistical inference, linear correlation, introduction to nonparametric statistical methods, and application to problems drawn from the natural and social sciences. Three hours of class per week. Three hours of class per week. | 3 |

MTH151 | Calculus I
This is the first course in the calculus sequence. Topics include differential and integral calculus for algebraic and trigonometirc functions with applications. Four hours of class per week. Prerequisite(s): MTH 105 and 106, or MTH 108, or equivalent. | 4 |

MTH152 | Calculus II
This is the second course in the calculus sequence. Topics include differential and integral calculus for the transcendental functions, advanced methods of integration, and infinite sequences and series. Prerequisite(s): MTH 151 | 4 |

MTH215W | Introduction to Proof
This course introduces students to the process of reading, understanding and writing rigorous mathematical arguments. Additionally, students will become familiar with computer software used for analyzing math problems and typesetting mathematical documents. This course is a pre-requisite for many upper-level math courses and is intended to help students transition from problem-solving oriented classes such as Calculus into courses focused on understanding and writing proofs. Topics include: basic logic, introductory set theory, functions and relations, and quantifiers. Prerequisite(s): MTH 151 and MTH 152, or equivalent, or permission of instructor. | 4 |

MTH221 | Linear Algebra
Topics include finite dimensional vector spaces, geometry of R, linear functions, systems of linear equations, and theory of matrices and determinants. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH222 | Multivariate and Vector Calculus
An introduction to multivariate calculus using vector spaces, partial differentiation and multiple integration, calculus of vector functions, applications to extremum problems, and differential equations. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH327 | Advanced Analysis
Foundations for abstract analysis, real and complex number systems, elements of point set topology and limits, continuity, and derivatives. Prerequisite(s): MTH 222 or equivalent. | 3 |

MTH341 | Abstract Algebra
Introduction to elements of modern abstract algebra, including rings, groups, and fields. Prerequisite(s): MTH 221 or equivalent. | 3 |

MTH498 | Tutorial: Mathematics
| 4 |

MTH499 | Tutorial: Mathematics
| 4 |

4 additional 200-level or above physics or mathematics courses approved in advance. |

## + Major Requirements (B.S. Degree)

## 60 credits, including: |
||

CMP202 | Introduction to Programming
An introduction to programming using C++ for students with no previous computer programming experience. Includes introduction to algorithms and object-oriented programming techniques. Prerequisite(s): CMP 140 or permission of the instructor | 3 |

IND350 | Scientific Research Methods
This course serves as an introduction to research literature and research methodology in the sciences. Students prepare a research proposal including literature review, experimental design and methods, budget, timetable, and bibliography. Other topics include professional presentation techniques and research ethics. The student's major department must approve proposals prior to the Tutorial. Prerequisite(s): Junior status and completion of at least two courses at the 200-level or above in the major, or permission of the instructor. | 2 |

MTH110 | Elementary Statistics
Topics include statistical measures and distributions, decision making under uncertainty, application of probability to statistical inference, linear correlation, introduction to nonparametric statistical methods, and application to problems drawn from the natural and social sciences. Three hours of class per week. Three hours of class per week. | 3 |

MTH151 | Calculus I
This is the first course in the calculus sequence. Topics include differential and integral calculus for algebraic and trigonometirc functions with applications. Four hours of class per week. Prerequisite(s): MTH 105 and 106, or MTH 108, or equivalent. | 4 |

MTH152 | Calculus II
This is the second course in the calculus sequence. Topics include differential and integral calculus for the transcendental functions, advanced methods of integration, and infinite sequences and series. Prerequisite(s): MTH 151 | 4 |

MTH215W | Introduction to Proof
This course introduces students to the process of reading, understanding and writing rigorous mathematical arguments. Additionally, students will become familiar with computer software used for analyzing math problems and typesetting mathematical documents. This course is a pre-requisite for many upper-level math courses and is intended to help students transition from problem-solving oriented classes such as Calculus into courses focused on understanding and writing proofs. Topics include: basic logic, introductory set theory, functions and relations, and quantifiers. Prerequisite(s): MTH 151 and MTH 152, or equivalent, or permission of instructor. | 4 |

MTH221 | Linear Algebra
Topics include finite dimensional vector spaces, geometry of R, linear functions, systems of linear equations, and theory of matrices and determinants. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH222 | Multivariate and Vector Calculus
An introduction to multivariate calculus using vector spaces, partial differentiation and multiple integration, calculus of vector functions, applications to extremum problems, and differential equations. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH327 | Advanced Analysis
Foundations for abstract analysis, real and complex number systems, elements of point set topology and limits, continuity, and derivatives. Prerequisite(s): MTH 222 or equivalent. | 3 |

MTH341 | Abstract Algebra
Introduction to elements of modern abstract algebra, including rings, groups, and fields. Prerequisite(s): MTH 221 or equivalent. | 3 |

MTH498 | Tutorial: Mathematics
| 4 |

MTH499 | Tutorial: Mathematics
| 4 |

PHY251 | Principles of Physics I
Introduction to the concepts, laws, and structure of physics. This is the first course in a calculus-based sequence that focuses on classical mechanics. Topics include vector analysis, kinematics, Newton’s laws, work, conservation of energy and momentum, collisions, gravity, harmonic motion, and wave phenomena. Prerequisite(s) or Corequisite: MTH 151. | 4 |

PHY252 | Principles of Physics II
Introduction to the concepts, laws, and structure of physics. The second course in a calculus-based physics sequence. Topics include thermodynamics, fluids, electricity, circuit analysis, magnetism, Maxwell’s equations, properties of light, and optics. Four hours of class per week. | 4 |

PHY255 | Physics Laboratory I
Experimental techniques of classical mechanical physics. Three hours of laboratory per week. | 1 |

PHY256 | Physics Laboratory II
Experimental techniques of classical physics with applications to electricity, magnetism, sound, and optics. Three hours per week. | 1 |

One of the following pairs of courses: |
||

BIO143 | The Cell
This course is designed to provide a broad overview of current biological concepts, including cell structure, function, division, and basic genetics. Biologically important molecules also are presented. This course is a prerequisite for all upper-level biology courses. Three hours of class | 3 |

BIO143L | Lab: The Cell
Experiments to complement the material presented in BIO143. Two hours of laboratory per week. Corequisite or prerequisite: BIO143. Additional Fee(s): Laboratory fee. | 1 |

BIO144 | The Organism
This course provides a general survey of animals and plants at the organismic level, with emphasis on their evolution and various physiological processes such as respiration, circulation, digestion, and reproduction. This course is a prerequisite for all upper-level biology courses. Three hours of class. | 3 |

BIO144L | Lab: The Organism
Experiments to complement the material presented in BIO144. Two hours of laboratory per week. Corequisite or prerequisite: BIO144. Additional Fee(s): Laboratory fees. | 1 |

CHM105 | General Chemistry
This class covers the same material as Chemistry 107 below, but is specifically structured for students who have had little or no previous chemistry experience, or who need extra help with algebraic problem solving. Three hours of lecture and one hour of recitation per week. Co-requisite: CHM 109 | 3 |

CHM109 | Chemistry I Laboratory
Introduction to the basic experimental procedures and laboratory techniques in chemistry. Experiments are correlated with the lectures in Chemistry 105 and Chemistry 107. Three hours of laboratory per week. Corequisite: CHM 105 or 107. Additional Fee(s): Laboratory fee. | 1 |

CHM107 | Chemistry I
This class begins with a study of atomic structure, then expands to cover chemical naming, patterns of reactivity, thermochemistry, the interaction of light and matter, atomic orbitals, ionic and covalent bonding, and molecular shapes. This class concludes with an introduction to organic chemistry and biochemistry. Three hours of lecture per week. Co-requisite: CHM 109 | 3 |

CHM109 | Chemistry I Laboratory
Introduction to the basic experimental procedures and laboratory techniques in chemistry. Experiments are correlated with the lectures in Chemistry 105 and Chemistry 107. Three hours of laboratory per week. Corequisite: CHM 105 or 107. Additional Fee(s): Laboratory fee. | 1 |

4 additional 200-level or above mathematics courses approved in advance. |

## + Interdisciplinary Major Requirements

## 8 courses, including: |
||

MTH151 | Calculus I
This is the first course in the calculus sequence. Topics include differential and integral calculus for algebraic and trigonometirc functions with applications. Four hours of class per week. Prerequisite(s): MTH 105 and 106, or MTH 108, or equivalent. | 4 |

MTH152 | Calculus II
This is the second course in the calculus sequence. Topics include differential and integral calculus for the transcendental functions, advanced methods of integration, and infinite sequences and series. Prerequisite(s): MTH 151 | 4 |

MTH221 | Linear Algebra
Topics include finite dimensional vector spaces, geometry of R, linear functions, systems of linear equations, and theory of matrices and determinants. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH222 | Multivariate and Vector Calculus
An introduction to multivariate calculus using vector spaces, partial differentiation and multiple integration, calculus of vector functions, applications to extremum problems, and differential equations. Three hours of class per week. Prerequisite(s): MTH 152 | 3 |

MTH327 | Advanced Analysis
Foundations for abstract analysis, real and complex number systems, elements of point set topology and limits, continuity, and derivatives. Prerequisite(s): MTH 222 or equivalent. | 3 |

MTH341 | Abstract Algebra
Introduction to elements of modern abstract algebra, including rings, groups, and fields. Prerequisite(s): MTH 221 or equivalent. | 3 |

3 additional courses approved in advance are required. The tutorial must combine mathematics and the cooperating program. |

## + Minor Requirements

## 6 courses, including: |
||

MTH151 | Calculus I
| 4 |

MTH152 | Calculus II
| 4 |

MTH221 | Linear Algebra
| 3 |

MTH222 | Multivariate and Vector Calculus
| 3 |

1 200-level or above course in mathematics approved in advance. 1 200-level or above course in computing, mathematics, or physics that has not been counted already toward a major or minor. |