Mathematics (BS)

The mathematics curriculum at Notre Dame includes six course sequences or areas of concentration within the College of Science. These programs are designed to accommodate the academic and professional interests of all mathematics majors. Brief descriptions are given below, and more detailed descriptions of these programs are available on request from the Department of Mathematics.

College Requirements

All must take the following:

College of Science Courses
CHEM 10171
CHEM 11171
Introduction to Chemical Principles
and Introduction to Chemical Principles Laboratory
4
CHEM 10172
CHEM 11172
Organic Structure and Reactivity
and Organic Structure and Reactivity Laboratory
4
or CHEM 10122 General Chemistry: Fundamental Principles and Biological Processes
PHYS 10310/10093Engineering Physics I: Mechanics 14
PHYS 10320/10094Engineering Physics II: Electromagnetism 14
Science Elective3
1

A student who takes two semesters of organic chemistry or two semesters of general biology is only required to take PHYS 30210 Physics I (or PHYS 10095) and Physics for Life Sciences II (PHYS 10096)

Mathematics Core Courses

All other mathematics programs (except the computing program) require the following mathematics core courses:

MATH 10550Calculus I4
MATH 10560Calculus II4
MATH 20550Calculus III3.5
MATH 20750Ordinary Differential Equations3
or MATH 30530 Introduction to Probability
MATH 20610Linear Algebra3
MATH 20630Introduction to Mathematical Reasoning3
MATH 30710Algebra3
MATH 30750Real Analysis3

Mathematics Career Program

This program is designed to give students a general background in mathematics. In addition to the basic sequence of courses listed above, 15 credit hours of mathematics electives are required, at least three of which are at the 40000 level.

Sample Curriculum Mathematics Career Program

Plan of Study Grid
First Year
First SemesterHours
MATH 10550 Calculus I 4
CHEM 10171
CHEM 11171
Introduction to Chemical Principles
and Introduction to Chemical Principles Laboratory
4
PHYS 10310 Engineering Physics I: Mechanics 4
University Requirement 3
University Requirement 3
Moreau First Year Experience 1
 Hours19
Second Semester
MATH 10560 Calculus II 4
CHEM 10172
CHEM 11172
Organic Structure and Reactivity
or General Chemistry: Fundamental Principles and Biological Processes
4
PHYS 10320 Engineering Physics II: Electromagnetism 4
University Requirement 3
University Requirement 3
 Hours18
Sophomore Year
First Semester
MATH 20610 Linear Algebra 3
MATH 20550 Calculus III 3.5
Language 3
University Requirement 3
Science Elective 3
 Hours15.5
Second Semester
MATH 20630 Introduction to Mathematical Reasoning 3
MATH 20750 Ordinary Differential Equations 3
Mathematics Elective 3
Language 3
University Requirement 3
 Hours15
Junior Year
First Semester
MATH 30710 Algebra 3
Mathematics Elective 3
Language 3
University Requirement 3
Elective 3
 Hours15
Second Semester
MATH 30750 Real Analysis 3
University Requirement 3
Electives 9
 Hours15
Senior Year
First Semester
Mathematics Electives 6
Electives 9
 Hours15
Second Semester
Mathematics Elective 3
Electives 9
Moreau Senior Capstone 1
 Hours13
 Total Hours125.5

Mathematics: Life Science Concentration

This program is designed for mathematics majors who are interested in life-science-oriented careers.

The following mathematics courses are required in addition to the basic sequence of courses listed above:

Mathematics Courses
MATH 30530Introduction to Probability3
MATH/ACMS 30540Mathematical Statistics3
40000 level Mathematics Elective3
College of Science Life Sciences Courses
CHEM 20273
CHEM 21273
Organic Reactions and Applications
and Organic Reactions and Applications Laboratory
4
CHEM 20274
CHEM 21274
Chemistry across the Periodic Table
and Chemistry Across the Periodic Table Laboratory
4
BIOS 10171
BIOS 11173
Biology I :Big Questions
and Biological Investigations Laboratory
4
BIOS 10172
BIOS 11174
Biology II: Molecules to Ecosystems
and Research Experience in Biology Laboratory
4
BIOS 20303
BIOS 21303
Fundamentals of Genetics
and Fundamental Genetics Laboratory
4

Mathematics and Computing Program

This program is designed for students who plan to pursue graduate study or industrial careers in computing science. 

Mathematics electives: at least three hours of which are at the 40000 level15
CSE courses
CSE 20311Fundamentals of Computing4
CSE 20312Data Structures3.5
CSE Electives (3 Courses)9

Mathematics Education Program

This program is designed for students who plan a career in secondary education. The following mathematics courses are required in addition to the basic sequence listed above:

MATH 30530Introduction to Probability3
MATH/ACMS 30540Mathematical Statistics3
Geometry (MATH 361 at Saint Mary's College)3
Discrete Math: 13
Introduction to Operations Research
Basic Combinatorics
Mathematics Elective 13
Education Courses taken at Saint Mary's College 230
Total Hours45
1

One of these classes must be at the 40000 level

2

The following education courses are to be taken at Saint Mary’s College: EDUC 201, 220, 340, 345, 346, 356, 451, and 475.

Mathematics and Engineering Science Program

This program is designed for students interested in applied or industrial mathematics. In addition to the mathematics core courses, the student is required to take:

Select one of the following:3
Complex Variables
Numerical Analysis
Partial Differential Equations
Mathematics Electives12
Select one of the following:15
Thermal Sequence
Mechanics I
and Mechanics II
and Fluid Mechanics
and Thermodynamics
and Heat Transfer
Structures and Design Sequence
Mechanics I
and Solid Mechanics
and Thermodynamics
and Introduction to Structural Engineering
and Structural Analysis
Total Hours30

The Senior Thesis for Mathematics Majors

Students in the mathematics program have the option of writing a thesis on a subject in mathematics, or in an interdisciplinary area connected to mathematics. Such a thesis is strongly encouraged for math honors students and is intended to give the student a better sense of how mathematics is done and used, and to develop in the student the habit of learning mathematics and its applications in an independent setting. In most cases, this work would be expected to be expository, but based on advanced level readings. It should represent an effort that goes beyond what is found in an undergraduate course. It is especially desirable for a student to present a somewhat novel approach to an established subject, or to explore one of the many interesting connections that mathematics has with other disciplines.

In the second semester of the junior year and the first semester of the senior year, the student will work closely with a faculty advisor on a program of readings in preparation for the thesis. The thesis is to be crafted during the second semester of the senior year, and must be submitted to the Director of Undergraduate Studies by April 15 of the senior year. If the thesis is approved, the citation of “Graduation with Senior Thesis” will appear on the student’s transcript.

In the second semester of the junior and senior years, the student attends the senior thesis writing seminar MATH 48900 Thesis, while in the first semester of the senior year, the student receives credit for MATH 48800 Undergraduate Research

Students interested in writing a senior thesis should contact the director of undergraduate studies in the Department of Mathematics.

Mathematics Honors Program

This program is suited to students who are interested in graduate work in one of the mathematical sciences and to those whose career plans require a strong background in modern mathematics.

MATH 10850Honors Mathematics I4
MATH 10860Honors Mathematics II4
MATH 20850Honors Mathematics III4
MATH 20860Honors Mathematics IV4
MATH 20810Honors Algebra I3
MATH 20820Honors Algebra II3
MATH 30810Honors Algebra III3
MATH 30820Honors Algebra IV3
MATH 30850Honors Analysis I3
MATH 30860Honors Analysis II3
Electives 112
Total Hours46
1

Six credit hours at the 40000 level