Major
The requirements for a major in mathematics vary according to the objectives of the student. There are seven courses required of all mathematics majors.
An additional four courses are required, selected from one of the following track options:
- Core Mathematics
- Applied Analysis
- Computational Mathematics
- Probability and Statistics
- Mathematical Economics
- Individualized
Writing Requirement
In order to satisfy the College of Arts and Sciences writing requirement, students majoring in mathematics must obtain writing credit in one of the following courses: MTH 433, MTH 461, MTH 502, MTH 504, MTH 520, MTH 533, MTH 561, and in three more writing courses from other departments.
Curriculum Requirements
The requirements of a major in mathematics vary according to the objectives of the student. There are seven courses required of all mathematics majors. An additional four courses are required selected from one of six track options:
Core Courses and Track Options
Code | Title | Credit Hours |
---|---|---|
Courses Required for All Mathematics Majors | ||
MTH 161 | Calculus I | 4 |
or MTH 171 | Calculus I | |
MTH 162 | Calculus II | 4 |
or MTH 172 | Calculus II | |
MTH 210 | Introduction to Linear Algebra | 3 |
MTH 230 | Introduction to Abstract Mathematics | 3 |
MTH 310 | Multivariable Calculus | 3 |
MTH 461 | Survey of Modern Algebra | 3 |
or MTH 561 | Abstract Algebra I | |
MTH 433 | Advanced Calculus | 3 |
or MTH 533 | Introduction to Real Analysis I | |
Track Options | ||
Select four courses from one of the following Tracks: | 12 | |
Core Mathematics Track: | ||
Select four of the following: | ||
Linear Algebra | ||
Elementary Complex Analysis | ||
Topology I | ||
Topology II | ||
Introduction to Real Analysis II | ||
Introduction to Differential Geometry | ||
Abstract Algebra II | ||
Applied Analysis Track: ^{1} | ||
Introduction to Ordinary Differential Equations | ||
Elementary Complex Analysis | ||
Select one of the following sequences: | ||
Partial Differential Equations I and Partial Differential Equations II | ||
Ordinary Differential Equations and Dynamics and Bifurcations | ||
Computational Mathematics Track: | ||
Introduction to Numerical Analysis | ||
Data Structures and Algorithm Analysis | ||
Numerical Linear Algebra and Numerical Methods in Differential Equations | ||
Probability and Statistics Track: | ||
Introduction to Probability and Statistics | ||
Introduction to Probability and Introduction to Mathematical Statistics | ||
Statistical Analysis | ||
Mathematical Economics Track: | ||
Introduction to Probability and Introduction to Mathematical Statistics | ||
Advanced Microeconomic Theory | ||
Select one of the following: | ||
Topics in Mathematical Economics | ||
Advanced Econometrics | ||
Advanced Macroeconomic Theory | ||
Individualized Track: | ||
Select one of the following: | ||
Introduction to Probability and Statistics | ||
Introduction to Ordinary Differential Equations | ||
Introduction to Numerical Analysis | ||
Select three of the following: ^{2} | ||
Linear Algebra | ||
Elementary Complex Analysis | ||
Partial Differential Equations I | ||
Partial Differential Equations II | ||
Ordinary Differential Equations | ||
Dynamics and Bifurcations | ||
Numerical Linear Algebra | ||
Numerical Methods in Differential Equations | ||
Introduction to Probability | ||
Introduction to Mathematical Statistics | ||
Topology I | ||
Topology II | ||
Introduction to Real Analysis II | ||
Statistical Analysis | ||
Introduction to Mathematical Finance | ||
Introduction to Differential Geometry | ||
Abstract Algebra II | ||
General Education Requirements | ||
Written Communication Skills: | ||
WRS 105 | First-Year Writing I | 3 |
WRS 106 | First-Year Writing II | 3 |
or ENG 106 | Writing About Literature and Culture | |
Quantitative Skills: | ||
Fulfilled through the Math Major | ||
Areas of Knowledge: | ||
Arts & Humanities Cognate | 9 | |
People & Society Cognate | 9 | |
STEM Cognate (9 credits) (fulfilled through the major) | ||
Other Requirements ^{3,4} | ||
Second Language courses ^{5} | 3 | |
Approved Natural Science course ^{6} | 3 | |
Minor or additional major | 15-35 | |
Electives ^{7} | 40-14 | |
Total Credit Hours | 120 |
- ^{ 1 }
Course work in physics is desirable.
- ^{ 2 }
It is possible to select other 500 level mathematics courses among the three, with prior approval of the Mathematics Department.
- ^{ 3 }
For the Additional Major in Mathematics, students not in the College of Arts and Sciences should use the requirements of their school or college's degree in place of the other requirements listed here.
- ^{ 4 }
The 120 credits must include a writing intensive course in mathematics and three writing intensive courses from other departments, not including WRS 105, WRS 106 WRS 107 and ENG 106.
- ^{ 5 }
Three credits in a language other than English at 200-level or higher are required. Prerequisites may be required.
- ^{ 6 }
For BS in Mathematics, the credits must be from Biology, Chemistry, Geological Sciences or Physics in a course that counts towards a major in that department. For BA in mathematics, the credits must be earned from Biology, Chemistry, Ecosystem Science & Policy (only ECS 111, ECS 112, or ECS 202), Geological Sciences, Marine Sciences (except MSC 313 and MSC 314), Physical Science or Physics. APY 203 and GEG 120 may also count.
- ^{ 7 }
For BS in Mathematics, electives must include MTH 224 or CSC 120.
- *
Notes
- It would be useful for students planning to do graduate study in mathematics to complete the following courses: MTH 531, MTH 532, MTH 533, MTH 534, MTH 561, MTH 562.
- Students interested in actuarial science should choose the Probability and Statistics option; for these students a finance minor is recommended.
- Transfer students will be permitted to apply up to 14 transfer credit hours towards the major; however, the courses MTH 461 (or MTH 561) and MTH 433 (or MTH 533) must be completed at the University of Miami.
- A grade of C- or better is required for each course applied toward the major; the overall quality point average for University of Miami courses applied toward the major must be 2.5 or above.
Requirements for Departmental Honors in Mathematics:
Code | Title | Credit Hours |
---|---|---|
Select three of the following sequences | 18 | |
MTH 513 & MTH 514 | Partial Differential Equations I and Partial Differential Equations II | 6 |
MTH 515 & MTH 516 | Ordinary Differential Equations and Dynamics and Bifurcations | 6 |
MTH 520 & MTH 521 | Numerical Linear Algebra and Numerical Methods in Differential Equations | 6 |
MTH 524 & MTH 525 | Introduction to Probability and Introduction to Mathematical Statistics | 6 |
MTH 531 & MTH 532 | Topology I and Topology II | 6 |
MTH 533 & MTH 534 | Introduction to Real Analysis I and Introduction to Real Analysis II | 6 |
MTH 561 & MTH 562 | Abstract Algebra I and Abstract Algebra II | 6 |
- *
The student must attain at least a B in each course used to fulfill this requirement. In addition, the student must attain at least a 3.5 average over all courses counted toward the mathematics major and an overall (university-wide) average of at least 3.3.
Possible Plan of Study
The B.A. and B.S. degrees in Mathematics differ only in the College of Arts and Sciences general education requirements. Here is a possible plan of study.
Year One | ||
---|---|---|
Fall | Credit Hours | |
MTH 161 | Calculus I | 4 |
WRS 105 | First-Year Writing I | 3 |
Language course | 3 | |
Select one of the following | 3 | |
Natural Science | ||
Elective | ||
Select one of the following | 3 | |
Cognate | ||
Elective | ||
Credit Hours | 16 | |
Spring | ||
MTH 162 | Calculus II | 4 |
MTH 210 | Introduction to Linear Algebra | 3 |
ENG 106 or WRS 106 | Writing About Literature and Culture or First-Year Writing II | 3 |
Language course | 3 | |
Select one of the followng | 3 | |
Natural Science | ||
Cognate | ||
Elective | ||
Credit Hours | 16 | |
Year Two | ||
Fall | ||
MTH 230 or 310 | Introduction to Abstract Mathematics or Multivariable Calculus | 3 |
Language course | 3 | |
Select one of the following | 3 | |
Natural Science | ||
Cognate | ||
Elective | ||
Select one of the following | 3 | |
Cognate | ||
Elective | ||
Elective | 3 | |
Credit Hours | 15 | |
Spring | ||
MTH 310 or 230 | Multivariable Calculus or Introduction to Abstract Mathematics | 3 |
Select one of the following | 3 | |
Mathematics 200 0r 300- level track course | ||
Cognate | ||
Elective | ||
Cognate | 3 | |
Electives | 6 | |
Credit Hours | 15 | |
Year Three | ||
Fall | ||
Select one of the following | 3 | |
Advanced Calculus | ||
Introduction to Real Analysis I | ||
Mathematics track course | ||
Select one of the following | 3 | |
Abstract Algebra I | ||
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Mathematics track course | ||
Elective | ||
Cognate | 3 | |
Elective | 3 | |
Credit Hours | 15 | |
Spring | ||
Select one of the following | 3 | |
Survey of Modern Algebra | ||
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Cognate | ||
Elecitve | ||
Electives | 6 | |
Credit Hours | 15 | |
Year Four | ||
Fall | ||
Select one of the following | 3 | |
Advanced Calculus | ||
Introduction to Real Analysis I | ||
Mathematics track course | ||
Select one of the following | 3 | |
Abstract Algebra I | ||
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Mathematics track course | ||
Cognate | ||
Elective | ||
Elective | 3 | |
Credit Hours | 15 | |
Spring | ||
Select one of the following | 3 | |
Survey of Modern Algebra | ||
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Mathematics track course | ||
Elective | ||
Select one of the following | 3 | |
Cognate | ||
Elective | ||
Electives | 6 | |
Credit Hours | 15 | |
Total Credit Hours | 122 |
Mission
The objective of the Bachelor’s degree in mathematics is to provide students with a core knowledge of mathematics essential to the understanding of science and other disciplines.
Goals
Students should gain substantial problem solving and critical reasoning skills, and they should develop an understanding of the conceptual underpinnings of mathematics. The knowledge gained through this program should provide the necessary background in mathematics for those students planning to go on to graduate study in mathematics and related fields. This knowledge should also prepare those students who will be immediately entering careers in science, business, education or other fields which are increasingly making use of mathematics.
Student Learning Outcomes
- Students will demonstrate an understanding of elementary real analysis and advanced calculus. They will understand the nature of analytic reasoning and logical analytic proofs. They will develop the ability to communicate ideas in analysis, and, in particular, the ability to formulate and present abstract arguments in analysis.
- Students will demonstrate an understanding of modern abstract algebra. They will understand the nature of algebraic reasoning and logical algebraic proofs. They will develop the ability to communicate algebraic ideas, and, in particular, the ability to formulate and present abstract algebraic arguments.
- Students will acquire a solid understanding of advanced material within a mathematics “specialty path” which synthesizes and extends their lower-division work. The path is selected by the individual student depending on his/her particular interests.