http://www.math.miami.edu

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 433MTH 461MTH 502MTH 504MTH 520MTH 533MTH 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

Courses Required for All Mathematics Majors
MTH 161Calculus I4
or MTH 171 Calculus I
MTH 162Calculus II4
or MTH 172 Calculus II
MTH 210Introduction to Linear Algebra3
MTH 230Introduction to Abstract Mathematics3
MTH 310Multivariable Calculus3
MTH 461Survey of Modern Algebra3
or MTH 561 Abstract Algebra I
MTH 433Advanced Calculus3
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 105First-Year Writing I3
WRS 106First-Year Writing II3
or ENG 106 Writing About Literature and Culture
Quantitative Skills:
Fulfilled through the Math Major
Areas of Knowledge:
Arts & Humanities Cognate9
People & Society Cognate9
STEM Cognate (9 credits) (fulfilled through the major)
Other Requirements 3,4
Second Language courses 53
Approved Natural Science course 63
Minor or additional major15-35
Electives 740-14
Total Credit Hours120
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 531MTH 532MTH 533MTH 534MTH 561MTH 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:

Select three of the following sequences18
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.

Plan of Study Grid
Year One
FallCredit 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 Hours16
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 Hours16
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 Hours15
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 Hours15
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 Hours15
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 Hours15
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 Hours15
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 Hours15
 Total Credit Hours122

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.