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:
Code | Title | Hours |
---|---|---|
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 10310/10093 | Engineering Physics I: Mechanics 1 | 4 |
PHYS 10320/10094 | Engineering Physics II: Electromagnetism 1 | 4 |
Science Elective | 3 |
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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:
Code | Title | Hours |
---|---|---|
MATH 10550 | Calculus I | 4 |
MATH 10560 | Calculus II | 4 |
MATH 20550 | Calculus III | 3.5 |
MATH 20750 | Ordinary Differential Equations | 3 |
or MATH 30530 | Introduction to Probability | |
MATH 20610 | Linear Algebra | 3 |
MATH 20630 | Introduction to Mathematical Reasoning | 3 |
MATH 30710 | Algebra | 3 |
MATH 30750 | Real Analysis | 3 |
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
First Year | ||
---|---|---|
First Semester | Hours | |
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 | |
Hours | 19 | |
Second Semester | ||
MATH 10560 | Calculus II | 4 |
CHEM 10172 & CHEM 11172 or CHEM 10122 |
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 | |
Hours | 18 | |
Sophomore Year | ||
First Semester | ||
MATH 20610 | Linear Algebra | 3 |
MATH 20550 | Calculus III | 3.5 |
Language | 3 | |
University Requirement | 3 | |
Science Elective | 3 | |
Hours | 15.5 | |
Second Semester | ||
MATH 20630 | Introduction to Mathematical Reasoning | 3 |
MATH 20750 | Ordinary Differential Equations | 3 |
Mathematics Elective | 3 | |
Language | 3 | |
University Requirement | 3 | |
Hours | 15 | |
Junior Year | ||
First Semester | ||
MATH 30710 | Algebra | 3 |
Mathematics Elective | 3 | |
Language | 3 | |
University Requirement | 3 | |
Elective | 3 | |
Hours | 15 | |
Second Semester | ||
MATH 30750 | Real Analysis | 3 |
University Requirement | 3 | |
Electives | 9 | |
Hours | 15 | |
Senior Year | ||
First Semester | ||
Mathematics Electives | 6 | |
Electives | 9 | |
Hours | 15 | |
Second Semester | ||
Mathematics Elective | 3 | |
Electives | 9 | |
Moreau Senior Capstone | 1 | |
Hours | 13 | |
Total Hours | 125.5 |
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:
Code | Title | Hours |
---|---|---|
Mathematics Courses | ||
MATH 30530 | Introduction to Probability | 3 |
MATH/ACMS 30540 | Mathematical Statistics | 3 |
40000 level Mathematics Elective | 3 | |
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.
Code | Title | Hours |
---|---|---|
Mathematics electives: at least three hours of which are at the 40000 level | 15 | |
CSE courses | ||
CSE 20311 | Fundamentals of Computing | 4 |
CSE 20312 | Data Structures | 3.5 |
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:
Code | Title | Hours |
---|---|---|
MATH 30530 | Introduction to Probability | 3 |
MATH/ACMS 30540 | Mathematical Statistics | 3 |
Geometry (MATH 361 at Saint Mary's College) | 3 | |
Discrete Math: 1 | 3 | |
Introduction to Operations Research | ||
or MATH 40210 | Basic Combinatorics | |
Mathematics Elective 1 | 3 | |
Education Courses taken at Saint Mary's College 2 | 30 | |
Total Hours | 45 |
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One of these classes must be at the 40000 level
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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:
Code | Title | Hours |
---|---|---|
Select one of the following: | 3 | |
Complex Variables | ||
Numerical Analysis | ||
Partial Differential Equations | ||
Mathematics Electives | 12 | |
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 Hours | 30 |
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.
Code | Title | Hours |
---|---|---|
MATH 10850 | Honors Mathematics I | 4 |
MATH 10860 | Honors Mathematics II | 4 |
MATH 20850 | Honors Mathematics III | 4 |
MATH 20860 | Honors Mathematics IV | 4 |
MATH 20810 | Honors Algebra I | 3 |
MATH 20820 | Honors Algebra II | 3 |
MATH 30810 | Honors Algebra III | 3 |
MATH 30820 | Honors Algebra IV | 3 |
MATH 30850 | Honors Analysis I | 3 |
MATH 30860 | Honors Analysis II | 3 |
Electives 1 | 12 | |
Total Hours | 46 |
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Six credit hours at the 40000 level