Mathematics, Statistics and Computer Science

Transcription

1 Mathematics, Statistics and Computer Science 1 Mathematics, Statistics and Computer Science Chairperson: Rebecca Sanders, Ph.D. marquette.edu/mscs/ The Department of Mathematics, Statistics and Computer Science offers a unique interdisciplinary learning environment with areas of study ranging from pure and applied mathematics to computer science, statistics and mathematics education. The Mathematics major (MATH) explores the interplay between the pure theory and the practical applications of mathematics. The mathematics curriculum can be tailored to an individual's interests with a focus in pure mathematics, applied mathematics or actuarial science, statistics, as well as secondary education. In any case, the curriculum is designed to provide technical skills for growth within the discipline and for success in a wide variety of careers. The Computer Science major (COSC) provides students with an understanding of the central ideas and methods used to solve real problems with software. Students will practice the many skills required to build computer systems that address problems in scientific, engineering, and business domains. Most of all, the major aims to prepare students for long-term success in a rapidly changing field that provides the computer technology underpinning our modern world. The Computational Mathematics major (COMA) blends the subjects of computer science and applied mathematics, providing a balance which would otherwise require a double major to achieve. Furthermore, the curriculum teaches the skills necessary for careers in today's technical environment. Data Science is the emerging field that seeks to extract and quantify knowledge from data. The Data Science major (DTSC) integrates statistics and mathematics with computer science, allowing students to develop the knowledge and skills necessary to discover and quantify new knowledge from data. Those prepared to integrate advanced technology with modern statistical and mathematical practices have the opportunity to use in data in action to benefit society. Data scientists turn data into knowledge. The Mathematics for Elementary School Teachers major (MELT) is for College of Education students who are seeking teaching certification at the elementary school level, while obtaining strong mathematical preparation. This program is designed to prepare mathematics specialists who provide vision, focus and leadership in elementary schools. Bioinformatics is a field that lies at the intersection of biology, statistics, and computer science, which is focused on the generation and analysis of large biological datasets. The interdisciplinary Bioinformatics major (INBI) provides sufficient depth in both biology and computer science in order to approach problems in bioinformatics from the perspective of both parent fields Biology and Computer Science. The program is designed to prepare individuals to use the computational tools of bioinformatics to solve problems or analyze datasets in biological sciences. For more information about the interdisciplinary Bioinformatics major (INBI), visit the College of Arts and Sciences Interdisciplinary Majors and Minors section of the Undergraduate Bulletin. The Department of Mathematics, Statistics and Computer Science offers a five-year B.S./M.S. accelerated degree program in which students may obtain both a B.S. degree in Computer Science and the professional master of science (M.S.) degree in Computing in five years. In addition, together with the Graduate School of Management, the Department of Mathematics, Statistics and Computer Science offers a five-year B.S./M.B.A. accelerated degree program. Major in Mathematics The major in mathematics consists of 39 credit hours of mathematics courses, including five required MATH courses (18 credit hours); one MATH sequence (two courses - 6 credit hours); at least one course from each of the three groups (Group 1- Pure Mathematics, Group 2 - Applied Mathematics and Group 3 - Statistics, for a total of 9 credit hours); and 6 additional credit hours of upper division MATH courses. Students majoring in mathematics must also complete the following course in computer science: COSC 1010 Introduction to Computer Programming. Required Mathematics Courses: MATH 2450 Calculus 3 4 Choose one of the following sequences: 6 MATH 4120 & MATH 4121 Abstract Algebra 1 and Abstract Algebra 2

2 2 Mathematics, Statistics and Computer Science MATH 4200 & MATH 4201 MATH 4200 & MATH 4210 MATH 4200 & MATH 4450 MATH 4420 & MATH 4030 MATH 4500 & MATH 4510 MATH 4670 & MATH 4650 MATH 4700 & MATH 4710 Intermediate Analysis 1 and Intermediate Analysis 2 Intermediate Analysis 1 and Complex Variables Intermediate Analysis 1 and Topology Foundations of Geometry and Concepts in Geometry and Calculus from an Advanced Standpoint Theory of Differential Equations and Elementary Partial Differential Equations Applied Combinatorial Mathematics and Theory of Optimization Theory of Probability and Mathematical Statistics Choose at least one additional course from each of the three groups listed below: 9 Group 1 - Pure Mathematics MATH 4120 Abstract Algebra 1 MATH 4121 Abstract Algebra 2 MATH 4200 Intermediate Analysis 1 MATH 4201 Intermediate Analysis 2 MATH 4210 MATH 4320 MATH 4420 MATH 4450 Group 2 - Applied Mathematics MATH 3520 MATH 4500 MATH 4510 MATH 4540 MATH 4630 MATH 4650 MATH 4670 Group 3 - Statistics MATH 4700 MATH 4710 MATH 4720 MATH 4740 MATH 4760 MATH 4780 Complex Variables Theory of Numbers Foundations of Geometry Topology Operational Methods in Physics and Engineering Theory of Differential Equations Elementary Partial Differential Equations Numerical Analysis Mathematical Modeling and Analysis Theory of Optimization Applied Combinatorial Mathematics Theory of Probability Mathematical Statistics Statistical Methods Biostatistical Methods and Models Time Series Analysis Regression Analysis Choose 6 credit hours of upper-division MATH courses. 6 Total Credit Hours 39 Occasionally MATH 4931 Topics in Mathematics or Statistics may be approved as a substitute within a student s program of study for an above listed course. MATH 2350 Foundations of Mathematics is the preferred course for a MATH major. For those seeking a double major in COSC or a minor in COSC, MATH 2100 Discrete Mathematics will be accepted as a substitute. Typical Program for Mathematics Major Freshman MATH MATH

3 Mathematics, Statistics and Computer Science 3 ENGL COSC UCCS-Ind. & Social Behavior 3 ENGL Electives 3 UCCS-Histories of Cult./Soc. 3 Sophomore MATH MATH MATH PHIL UCCS-Literature / Performing Arts 3 UCCS-Science & Nature 3-4 Electives 6 Electives 6 Junior MATH Sequence (part 1) 3 MATH Sequence (part 2) 3 MATH Group 1 (Pure) 3 MATH Group 3 (Statistics) 3 THEO PHIL Electives 6 Electives 6 Senior MATH Group 2 (Applied) 3 MATH 3xxx/4xxx 3 MATH 3xxx/4xxx 3 UCCS-Diverse Cultures 3 UCCS-Theology 3 Electives 10 Electives 7 Total credit hours: Department of Public Instruction Certification for Mathematics Majors To pursue Department of Public Instruction certification, College of Education students are required to fulfill the requirements of a mathematics major (39 credit hours of mathematics courses) as listed below. In addition to the 39 credit hours, students must complete an introductory computer science course (4 credit hours), the mathematics teaching methodology course (3 credit hours), and the algebra and geometry course for middle school teachers (2 credit hours) for a total of 48 credit hours as listed below. Notes: Students majoring in mathematics must also complete COSC 1010 Introduction to Computer Programming MATH 4020 The Teaching of Mathematics is required as part of the state certification program and must be completed before student teaching. MATH 2032 Algebra and Geometry for Teachers is also required. From the beginning of their work toward a degree, students should consult with both the department adviser for Mathematics Education and the Director of Teacher Education in the College of Education about the appropriate sequence of courses. Required Mathematics Courses: MATH 2450 Calculus 3 4

4 4 Mathematics, Statistics and Computer Science MATH 4420 & MATH 4030 Required Group Courses: Group 1 - Pure Mathematics Foundations of Geometry and Concepts in Geometry and Calculus from an Advanced Standpoint MATH 4120 Abstract Algebra 1 3 Group 2 - Applied Mathematics MATH 4630 Mathematical Modeling and Analysis 3 Group 3 - Statistics MATH 4720 Statistical Methods 3 Additional Mathematics Courses: MATH 4670 Applied Combinatorial Mathematics 3 or MATH 4700 Theory of Probability MATH 4040 Concepts in High School Algebra and Number Theory from an Advance Standpoint 3 Total Credit Hours 39 Math B.S./M.B.A. Accelerated Degree Program The Department of Mathematics, Statistics and Computer Science together with the Graduate School of Management offers an accelerated degree program which allows students to earn both their B.S. degree in Math and a master of business administration (M.B.A.) all within in a five-year time period. During the first four years of the program, students complete both their coursework requirements for their Math B.S. degree and the necessary prerequisite courses for the M.B.A. degree in the College of Business Administration. In addition, undergraduate students begin their M.B.A. graduate work in their senior year by taking two graduate level courses. To be considered for admission to the B.S./M.B.A. five-year program, applicants must formally apply to the Graduate School of Management during their junior year at Marquette University. For more detailed information and details of a typical five-year coursework plan, please refer to the Graduate School of Management Bulletin and contact the Department of Math, Statistics and Computer Science or the Graduate School of Management. Major in Computational Mathematics The major in computational mathematics consists of 50 credit hours of computer science and mathematics courses as listed below: Required Computer Sciences Courses: COSC 1010 Introduction to Computer Programming 4 COSC 1020 Object-Oriented Software Design 4 COSC 2100 Data Structures and Algorithms 1 3 COSC 2200 Hardware Systems 3 Computer Science Elective: Choose one of the following. 3 COSC 3250 COSC 3410 Required Mathematics Courses: Operating Systems Programming Languages MATH 2450 Calculus 3 4 MATH 4540 Numerical Analysis 3 MATH 4630 Mathematical Modeling and Analysis 3 MATH 4710 Mathematical Statistics 3 or MATH 4720 Statistical Methods Mathematics Electives: Choose two of the following. 6 MATH 4200 Intermediate Analysis 1 MATH 4210 MATH 4500 MATH 4510 Complex Variables Theory of Differential Equations Elementary Partial Differential Equations 6

5 Mathematics, Statistics and Computer Science 5 MATH 4650 MATH 4670 MATH 4700 MATH 4740 MATH 4760 MATH 4780 Theory of Optimization Applied Combinatorial Mathematics Theory of Probability Biostatistical Methods and Models Time Series Analysis Regression Analysis Total Credit Hours 50 COSC 2100 Data Structures and Algorithms 1 is the preferred course for a COMA major, however COSC 2010 Data Structures for Engineers will be accepted as a substitute. Typical Program for Computational Mathematics Majors Freshman COSC COSC MATH MATH ENGL ENGL UCCS-Hist of Cultures & Soc. 3 UCCS-Indiv. & Soc. Behav. 3 Sophomore COSC MATH COSC PHIL MATH UCCS-Science & Nature 3-4 MATH Electives 6 Elective 3 Junior COSC 3410 (or elective) 3 COSC 3250 (or elective) 3 Mathematics elective 3 Mathematics elective 3 THEO PHIL UCCS-Lit./Performing Arts 3 Electives 6 Electives 3 Senior MATH MATH 4710 or MATH UCCS-Diverse Cultures 3 UCCS-Theology 3 Electives 9

6 6 Mathematics, Statistics and Computer Science Electives 7 Total credit hours: Major in Computer Science The major in computer science consists of nine required COSC courses (29 credit hours) and 12 credit hours of upper-division COSC elective courses, for a total of 41 credit hours of COSC courses. In addition, each student must complete 27 credit hours of mathematics and science, including four required MATH cognate courses (14 credit hours), a natural science elective with laboratory component (3-4 credit hours), and an additional 3 credit hours of upper-division MATH. Required Computer Science Courses: COSC 1010 Introduction to Computer Programming 4 COSC 1020 Object-Oriented Software Design 4 COSC 2100 Data Structures and Algorithms 1 3 COSC 2200 Hardware Systems 3 COSC 3100 Data Structures and Algorithms 2 3 COSC 3250 Operating Systems 3 COSC 3410 Programming Languages 3 COSC 4920 Principles of Design 3 COSC 4998 Senior Design Project 3 Electives - Choose 12 credit hours of upper-division COSC courses. 12 Required Mathematics Cognate Courses: MATH 2100 Discrete Mathematics 3 Mathematics Elective - Choose 3 additional credit hours of upper-division MATH. 3 Natural Science Elective with Laboratory Component - Choose at least 3 additional credit hours of BIOL, CHEM or PHYS with laboratory. 3 Math/Science Electives - Choose 7 additional credit hours of MATH, BIOL, CHEM or PHYS. 7 Total Credit Hours 68 Notes: MATH 2100 Discrete Mathematics is the preferred course for a COSC major. For those seeking a double major in MATH or a minor in MATH, MATH 2350 Foundations of Mathematics will be accepted as a substitute. COSC 2100 Data Structures and Algorithms 1 is the preferred course for a COSC major, however COSC 2010 Data Structures for Engineers can be substituted. Typical Program for Computer Science Majors Freshman COSC COSC MATH MATH ENGL ENGL THEO Natural Science with Laboratory 4 Sophomore COSC COSC

7 Mathematics, Statistics and Computer Science 7 COSC COSC MATH MATH UCCS-Lit./Performing Arts 3 PHIL Elective 3 Elective Junior COSC COSC 3xxx/4xxx 3 COSC 3xxx/4xxx 3 MATH 3xxx/4xxx 3 Math/Science elective 3-4 Math/Science elective 3-4 UCCS-Hist. of Cultures & Soc. 3 PHIL UCCS-Theology 3 Elective 3 Elective Senior COSC COSC COSC 3xxx/4xxx 3 COSC 3xxx/4xxx 3 UCCS-Indiv. & Soc. Behav. 3 UCCS-Diverse Cultures 3 Electives 6 Electives Total credit hours: Must complete 13 credit hours of Math/Science electives, including at least: 3 credit hours upper-division (3000- or 4000-level) MATH courses, 3 credit hours science course with a laboratory component (BIOL, CHEM or PHYS), and one course designated by the College of Arts & Sciences to meet the UCCS-Science and Nature requirement. Computer Science B.S./M.B.A. Accelerated Degree Programs The Department of Mathematics, Statistics and Computer Science offers an accelerated degree program where eligible students may obtain both their B.S. degree in Computer Science and a professional master of science (M.S.) degree in Computing in five years. Students are eligible to apply to this program as early as the final semester of their sophomore year. Students wishing to participate in the five-year program must apply and be admitted to the program before their senior year, when they begin to take graduate credits. Minimal criteria for application to the ADP include a GPA of at least in the following: two semesters of courses in programming; two semesters of courses on data structures and algorithms; and three courses in calculus and discrete mathematics. For more detailed information, please refer to the Graduate School Bulletin and contact the Department of Mathematics, Statistics and Computer Science. Together with the Graduate School of Management, the Department of Mathematics, Statistics and Computer Science offers an accelerated degree program which allows students to earn both their B.S. degree in Computer Science and a master of business administration (M.B.A.) all within in a fiveyear time period. During the first four years of the program, students complete both their coursework requirements for their Computer Science B.S. degree and the necessary prerequisite courses for the M.B.A. degree in the College of Business Administration. In addition, undergraduate students begin their M.B.A. graduate work in their senior year by taking two graduate level courses.

8 8 Mathematics, Statistics and Computer Science To be considered for admission to the B.S./M.B.A. five-year program, applicants must formally apply to the Graduate School of Management during their junior year at Marquette University. For more detailed information and details of a typical five-year coursework plan, please refer to the Graduate School of Management Bulletin and contact the Department of Mathematics, Statistics and Computer Science or the Graduate School of Management. Major in Data Science The major in data science consists of 59 credit hours of computer science and mathematics courses, including sixteen required courses (53 credit hours) and two computer science or mathematics electives (6 credit hours). Required Computer Science Courses: COSC 1010 Introduction to Computer Programming 4 COSC 1020 Object-Oriented Software Design 4 COSC 2100 Data Structures and Algorithms 1 3 COSC 4610 Data Mining 3 COSC 4800 Principles of Database Systems 3 COSC 4920 Principles of Design 3 COSC 4998 Senior Design Project 3 Required Mathematics Courses: or MATH 2100 Discrete Mathematics MATH 2450 Calculus 3 4 MATH 4700 Theory of Probability 3 Data Science and Data Visualization (New 2017) 3 MATH 4720 Statistical Methods 3 MATH 4780 Regression Analysis 3 Computer Science or Mathematics Electives: Choose two of the following. 6 COSC 4600 MATH 4630 MATH 4710 MATH 4760 Fundamentals of Artificial Intelligence Mathematical Modeling and Analysis Mathematical Statistics Time Series Analysis Total Credit Hours 59 Depending on course topic, COSC 4931 Topics in Computer Science or MATH 4931 Topics in Mathematics or Statistics may be substituted as a Data Science elective. Typical Program for Data Science Major Freshman COSC COSC MATH MATH ENGL ENGL UCCS-Science & Nature 4 UCCS-Hist. of Cultures & Soc. 3 Sophomore COSC MATH

9 Mathematics, Statistics and Computer Science 9 MATH MATH MATH Data Science and Data Visualization 3 UCCS-Lit./Performing Arts 3 UCCS-Indiv. & Soc. Behav. 3 Elective 3 Elective Junior COSC COSC MATH Data Science elective 3 PHIL PHIL Electives 6 THEO Elective Senior COSC COSC Data Science elective 3 MATH UCCS-Theology 3 UCCS-Diverse Cultures 3 Electives 6 Electives Total credit hours: 120 The above Typical Program for a data science major is for students entering Marquette in odd numbered years. For those students entering Marquette in even numbered years, switch the Data Science elective in second term of Junior year with MATH 4780 Regression Analysis in second term of Senior year. Major in Mathematics for Elementary School Teachers (MELT) This major is for students in the College of Education enrolled in the middle childhood/early adolescence teacher education program (grades 1-8). The major in mathematics for elementary teachers consists of twelve required mathematics courses for a total of 36 credit hours as listed below. From the beginning of their work toward a degree, students should consult with both a department adviser and the director of teacher education in the College of Education about the appropriate sequence of courses. University and state requirements for teacher certification are described in the College of Education section of this bulletin. Required Courses: MATH 2030 Problem Solving and Reasoning for Teachers 3 MATH 2031 Number Systems and Operations for Elementary Teachers 2 MATH 2032 Algebra and Geometry for Teachers 2 MATH 4310 History of Mathematical Ideas 3 MATH 4320 Theory of Numbers 3 MATH 4420 Foundations of Geometry 3

10 10 Mathematics, Statistics and Computer Science MATH 4630 Mathematical Modeling and Analysis 3 MATH 4720 Statistical Methods 3 Total Credit Hours 36 Typical Program for Mathematics for Elementary School Teachers Majors Freshman ARSC ARSC EDUC EDUC ENGL ENGL 1002 or COMM Foreign Language 1 4 Foreign Language 2 4 MATH MATH Service Learning Sophomore EDUC HIST 1301, 1401, or POSC EDUC Literature elective 3 PHIL MATH MATH HIST MATH 4310 or THEO THEO Field Experience Junior PHIL EDUC EDUC EDUC EDUC EDUC EDUC 4337 (must be taken for 3 cr. hrs.) 3 MATH MATH EDUC MATH MATH 4310 or Field Experience 2 MATH Field Experience Senior EDUC EDUC 4966 (must be taken for 15 cr. hrs.) 15 EDUC EDUC MATH

11 Mathematics, Statistics and Computer Science 11 EDUC MATH Senior Level Practicum Total credit hours: 142 A minimum of 128 credits is required for the degree. EDUC 4337 Teaching Elementary Social Studies must be taken for 3 cr. hrs. EDUC 4966 Student Teaching: Elementary/Middle must be taken for 15 cr. hrs. Minor in Mathematics The minor in mathematics consists of 24 credit hours of mathematics courses, including four required math courses (15 credit hours) and an additional 9 credit hours of upper division math courses as listed below. Required Courses: MATH 2450 Calculus 3 4 or MATH 2451 Differential Equations Electives - Choose at least nine additional hours of upper-division MATH courses. 9 Total Credit Hours 24 Department of Public Instruction Certification for Mathematics Minor To pursue Department of Public Instruction certification for a minor in mathematics, College of Education students are required to fulfill the requirements of the mathematics minor (24 credit hours of mathematics courses) as listed below. In addition to the 24 credit hours in mathematics, students must complete the mathematics teaching methodology course (3 credit hours), as listed below. Notes: MATH 4020 The Teaching of Mathematics is required as part of the state certification program and must be completed before student teaching. From the beginning of their work toward a degree, students should consult with both the department adviser for Mathematics Education and the director of Teacher Education in the College of Education about the appropriate sequence of courses. MATH 2350 Foundations of Mathematics is the preferred course for a MATH minor. For those seeking a major in COSC or a minor in COSC, MATH 2100 Discrete Mathematics can be substituted. Required Courses: MATH 2450 Calculus 3 4 MATH 4420 Foundations of Geometry 3 MATH 4720 Statistical Methods 3 Total Credit Hours 24 Minor in Computer Science The minor in computer science consists of 20 credit hours of computer science courses, including four required COSC courses (14 credit hours) and 6 additional credit hours of upper-division COSC elective courses. In addition, each student must complete a required MATH course (3 credit hours) as listed below: Required Courses: COSC 1010 Introduction to Computer Programming 4

12 12 Mathematics, Statistics and Computer Science COSC 1020 Object-Oriented Software Design 4 COSC 2100 Data Structures and Algorithms 1 3 COSC 2200 Hardware Systems 3 Electives - Choose 6 credit hours of upper-division COSC courses. 6 Required Mathematics Course: MATH 2100 Discrete Mathematics 3 Total Credit Hours 23 MATH 2100 Discrete Mathematics is the preferred course for a COSC minor. For those seeking a major in MATH or a minor in MATH, MATH 2350 Foundations of Mathematics can be substituted. COSC 2100 Data Structures and Algorithms 1 is the preferred course for a COSC minor, however COSC 2010 Data Structures for Engineers can be substituted. Minor in Software Development The minor in software development consists of 20 credit hours of computer science courses, including four required COSC courses (14 credit hours) and 6 additional credit hours of upper-division COSC elective courses. In addition, each student must complete a required MATH course (3 credit hours) as listed below: Required Courses: COSC 1010 Introduction to Computer Programming 4 COSC 1020 Object-Oriented Software Design 4 COSC 2100 Data Structures and Algorithms 1 3 COSC 4860 Component-Based Software Construction 3 Electives - Choose 6 credit hours of upper-division COSC courses. 6 Required Mathematics Course: MATH 2100 Discrete Mathematics 3 Total Credit Hours 23 MATH 2100 Discrete Mathematics is the preferred course for a Software Development minor. For those seeking a major in MATH or a minor in MATH, MATH 2350 Foundations of Mathematics can be substituted. COSC 2100 Data Structures and Algorithms 1 is the preferred course for a Software Development minor, however COSC 2010 Data Structures for Engineers can be substituted.