Program Overview

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Mathematics: Comprehensive Emphasis

Overview

If you find beauty in the theory of mathematics, learn how the Comprehensive emphasis can prepare you for graduate studies in math and science. Mathematicians can work as university professors, teaching and doing research, or in a variety of scientific fields. The Bachelor of Science or Bachelor of Arts in Mathematics with a Comprehensive emphasis serves as a launching pad for students wishing to attain a graduate degree in mathematics, mathematics education or applied math. Undergraduates immerse themselves in the study of abstract algebra, mathematical analysis and more. They learn to apply rigorous logic and creativity to mathematical problems. In addition, they must complete a minor outside of the Department of Mathematics. Students who major in comprehensive mathematics and another field should be well-prepared for graduate studies in either field.

Learning Outcomes

• Apply computational methods; Math majors should be able to apply computational methods and mathematical concepts to analyze scientific problems
• Apply mathematical models to current problems; Math majors should be able to critically evaluate and extend selected mathematical models in the current scientific literature.
• Create valid proofs; Students should be able to identify an appropriate proof strategy and almost always able to create a correct proof using multiple strategies as appropriate.
• Define Terms Precisely; Precision is essential in mathematics, and a crucial skill for math majors is to learn to define mathematical terms precisely.
• Effective communication of results; Math majors should be able to effectively communicate results to non-specialized audiences in written and verbal form.
• Recognize valid arguments; Logical rigor is a critical component of mathematical argumentation. We expect math majors to develop the ability to recognize when arguments are valid, and identify logical gaps and flaws.

Program Details

Sample Courses

• MATH 413: Linear Algebra
• MATH 415A: Introduction to Abstract Algebra
• MATH 425A: Real Analysis of One Variable

Career Fields

• Higher education
• Research
• Science
• Engineering
• Finance

Level of Math

arrowdownSubstantial Knowledge

This strand involves skill and facility with calculus. The S-strand begins at one of two calculus options - MATH 122A/B (Functions for Calculus and First-Semester Calculus) or MATH 125 (Calculus I). Students who successfully complete the S-strand may continue on to MATH 129 (Calculus II), MATH 223 (Vector Calculus), or beyond. Those who choose but are not ready to begin the S-strand will be required to take preparatory work.

Level of Second Language

arrowdown4th Semester Proficiency

Fourth-semester skill level in a second language is required. B.A. degree students may fulfill this requirement with one of the following options: 1. Scoring the equivalent of fourth-semester skill level on an entrance or placement examination administered by The University of Arizona. 2. Completion of a two-course sequence beyond the second semester of post-secondary language instruction. 3. Completion with a C or higher of a 300- or 400-level language course at the post-secondary level. 4. Completion of one course beyond the third semester in combination with an AP (Advanced Placement) score, IB (International Baccalaureate) score or a CLEP (College Level Entrance Program) score determined by the individual language department. 5. An AP, IB, or CLEP language score determined by individual language departments 6. A minimum of one semester study abroad in a language program approved by the appropriate language department as the equivalent of fourth-semester skill level.

Pre-major Required?

No

This Major's College

College of Science

Degree

Bachelor of Arts

Sample Plans

4-Year Sample Plan

• First Year
  • 1st Semester
    • MATH 122A Functions for Calculus
    • MATH 122B First-Semester Calculus
    • ENGL 101 - First Year Writing 1 (GE Foundation Composition)
    • GE Core: Exploring Perspectives or Building Connections
    • GE Foundation Second Language (First Semester)
    • UNIV 101 - Introduction to the General Education Experience (GE Entry)
  • 2nd Semester
    • MATH 129 Calculus II
    • Supporting Computer Science ex. CSC 110 Intro to Computer Programming I
    • ENGL 102 - First Year Writing 2 (GE Foundation Composition)
    • GE Core: Exploring Perspectives or Building Connections
    • GE Foundation Second Language (Second Semester)
• Second Year
  • 3rd Semester
    • MATH 223 Vector Calculus
    • MATH 313 Intro to Linear Algebra
    • GE Core: Exploring Perspectives or Building Connections
    • GE Core: Exploring Perspectives or Building Connections
    • GE Foundation Second Language (Third Semester)
  • 4th Semester
    • MATH 323 Formal Math Reasong + Wrtg
    • MATH 396L - required with MATH 323 in some cases
    • MATH 355 Anls Ord Diff Equations
    • GE Core: Exploring Perspectives or Building Connections
    • GE Foundation Second Language (Fourth Semester)
• Third Year
  • 5th Semester
    • MATH 425A Real Analy One Variable
    • MATH 413 Linear Algebra
    • Minor course
    • GE Core: Exploring Perspectives or Building Connections
    • GE Core: Exploring Perspectives or Building Connections
  • 6th Semester
    • MATH 425B Real Anls Several Vari
    • MATH 424 Thry of Complex Variable
    • Minor course
    • General Education Portfolio (Exit Course)
• Fourth Year
  • 7th Semester
    • Comprehensive Mathematics Emphasis Sequence Course ex. MATH 415A Introduction to Abstract Algebra
    • Minor course
    • Minor course
    • General Elective
    • General Elective
  • 8th Semester
    • Comprehensive Mathematics Emphasis Sequence Course ex. MATH 415B Second Course in Abstract Algebra
    • Minor course
    • Minor course
    • General Elective

Map Transfer Coursework

Enter your coursework from Arizona universities or community colleges to see how they can map to this major.

Connect with The University of Arizona Academic Advisors to validate how your coursework will transfer.

About the Transfer Mapping Categories

Maps to One Requirement

A transfer course with this designation matches a UAZ course that maps to one requirement for this major.

Can Map in Multiple Ways

A transfer course with this designation matches a UAZ course that maps to more than one requirement for this major. This means that the transfer course could meet any of the matching requirements but does not mean it fulfills all matching requirements.

Ask an Advisor

A transfer course with this designation matches a UAZ course that has not yet been mapped to a requirement for this major, or it means that the transfer course was input incorrectly.

Mapped Coursework

0 Maps to One Requirement

0 Can Map Multiple Ways

0 Ask An Advisor

*One course typically meets only one requirement

Mapped to Sample Plan Requirements

1st Semester

• MATH 122A Functions for Calculus
• MATH 122B First-Semester Calculus
• ENGL 101 - First Year Writing 1 (GE Foundation Composition)
• GE Core: Exploring Perspectives or Building Connections
• GE Foundation Second Language (First Semester)
• UNIV 101 - Introduction to the General Education Experience (GE Entry)

2nd Semester

• MATH 129 Calculus II
• Supporting Computer Science ex. CSC 110 Intro to Computer Programming I
• ENGL 102 - First Year Writing 2 (GE Foundation Composition)
• GE Core: Exploring Perspectives or Building Connections
• GE Foundation Second Language (Second Semester)

3rd Semester

• MATH 223 Vector Calculus
• MATH 313 Intro to Linear Algebra
• GE Core: Exploring Perspectives or Building Connections
• GE Core: Exploring Perspectives or Building Connections
• GE Foundation Second Language (Third Semester)

4th Semester

• MATH 323 Formal Math Reasong + Wrtg
• MATH 396L - required with MATH 323 in some cases
• MATH 355 Anls Ord Diff Equations
• GE Core: Exploring Perspectives or Building Connections
• GE Foundation Second Language (Fourth Semester)

5th Semester

• MATH 425A Real Analy One Variable
• MATH 413 Linear Algebra
• Minor course
• GE Core: Exploring Perspectives or Building Connections
• GE Core: Exploring Perspectives or Building Connections

6th Semester

• MATH 425B Real Anls Several Vari
• MATH 424 Thry of Complex Variable
• Minor course
• General Education Portfolio (Exit Course)

7th Semester

• Comprehensive Mathematics Emphasis Sequence Course ex. MATH 415A Introduction to Abstract Algebra
• Minor course
• Minor course
• General Elective
• General Elective

8th Semester

• Comprehensive Mathematics Emphasis Sequence Course ex. MATH 415B Second Course in Abstract Algebra
• Minor course
• Minor course
• General Elective