{
  "college": "napa-valley-college",
  "edition": "2026-2027",
  "code": "MATH",
  "name": "Mathematics",
  "sourceUrl": "https://catalog.napavalley.edu/courses/math/",
  "courses": [
    {
      "code": "MATH-C2210",
      "subject": "MATH",
      "number": "C2210",
      "title": "Calculus I: Early Transcendentals",
      "units": "5",
      "hours": "90 hours lecture; 90 hours total",
      "prerequisite": "Pre-calculus, or college algebra and trigonometry, or equivalent, or placement as determined by the college's multiple measures assessment process.",
      "advisory": "Completion of Math-110 with a minimum grade of C or appropriate placement.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "A first course in differential and integral calculus of a single variable. Topics include limits and continuity of functions, techniques and applications of differentiation, an introduction to integration, and the Fundamental Theorem of Calculus. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors. Formerly known as MATH 120.",
      "notes": [
        "Recommended Corequisite: Students who do not place directly into this course may enroll if they also enroll in the corresponding corequisite course."
      ],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 6,
          "open": 5,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-c2210"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 5,
          "open": 4,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-c2210"
        }
      ]
    },
    {
      "code": "MATH-C2220",
      "subject": "MATH",
      "number": "C2220",
      "title": "Calculus II: Early Transcendentals",
      "units": "5",
      "hours": "90 hours lecture; 90 hours total",
      "prerequisite": "Calculus I: Early Transcendentals (MATH-C2210), or equivalent, or placement as determined by the college's multiple measures assessment process.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "A second course in differential and integral calculus of a single variable. Topics include applications of integration, techniques of integration, infinite sequences and series, and the calculus of parametric and polar equations. This course is primarily intended for Science, Technology, Engineering, and Mathematics (STEM) majors. Formerly known as MATH 121.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 2,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-c2220"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 4,
          "open": 3,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-c2220"
        }
      ]
    },
    {
      "code": "MATH-81",
      "subject": "MATH",
      "number": "81",
      "title": "Support for Mathematical Concepts",
      "units": "1",
      "hours": "36 hours activity; 36 hours total",
      "cid": [],
      "transfer": [],
      "description": "This course is designed for students who seek additional mathematics support for courses where no designated linked corequisite support course is available, including but not limited to chemistry, business calculus, or precalculus. Topics include solving, simplifying, and performing operations, with an emphasis on building foundational skills to support success in concurrent coursework.",
      "notes": [
        "Recommended Corequisite: Enrollment is required for students who place into a transfer-level mathematics course and are designated to receive additional support when no linked corequisite support course is available."
      ],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-81"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-81"
        }
      ]
    },
    {
      "code": "MATH-86",
      "subject": "MATH",
      "number": "86",
      "title": "Support for College Algebra",
      "units": "2",
      "hours": "18 hours lecture; 36 hours activity; 54 hours total",
      "corequisite": "Concurrent enrollment in MATH-106 or equivalent.",
      "cid": [],
      "transfer": [],
      "description": "This course is open only to students concurrently enrolled in College Algebra. Concepts will be covered using a just-in-time approach for understanding of the corresponding concepts as they are presented in College Algebra. This course is designed to offer support for students who lack the strong algebra background needed to succeed in College Algebra.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-86"
        }
      ]
    },
    {
      "code": "MATH-87",
      "subject": "MATH",
      "number": "87",
      "title": "Support for Applied Calculus",
      "units": "1",
      "hours": "54 hours lab; 54 hours total",
      "corequisite": "Concurrent enrollment in MATH-115 or equivalent.",
      "cid": [],
      "transfer": [],
      "description": "This course is intended for students who are almost ready to succeed in Applied Calculus and for whom the just-in-time remediation will provide a foundation for success. Topics including functions, solving equations, graphing and simplifying expressions will be covered as needed.",
      "notes": [],
      "offered": []
    },
    {
      "code": "MATH-88",
      "subject": "MATH",
      "number": "88",
      "title": "Support for Calculus I",
      "units": "2",
      "hours": "18 hours lecture; 54 hours lab; 72 hours total",
      "prerequisite": "Concurrent enrollment in Math-120 or equivalent.",
      "cid": [],
      "transfer": [],
      "description": "Math-88, Support for Calculus I, is open only to students concurrently enrolled in Math-120, Calculus I. Concepts will be covered using a just-in-time approach for understanding of the corresponding concepts as they are presented in Math 120. Within this support course, students engage in a comprehensive review of algebraic and trigonometric concepts crucial for achieving success in Calculus I.",
      "notes": [],
      "offered": [
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-88"
        }
      ]
    },
    {
      "code": "MATH-106",
      "subject": "MATH",
      "number": "106",
      "title": "College Algebra",
      "units": "4",
      "hours": "54 hours lecture; 36 hours activity; 90 hours total",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course provides a college level study of polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations and analytic geometry.",
      "notes": [
        "Prerequisites or Corequisites: Placement as determined by the college's multiple measures assessment process or completion of a course taught at or above the level of intermediate algebra.",
        "Recommended Corequisite: Students who do not place directly into this course may enroll if they also enroll in the corresponding corequisite course."
      ],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 4,
          "open": 3,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-106"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-106"
        }
      ]
    },
    {
      "code": "MATH-108",
      "subject": "MATH",
      "number": "108",
      "title": "Trigonometry",
      "units": "3",
      "hours": "54 hours lecture; 54 hours total",
      "prerequisite": "Completion of MATH-106 with a minimum grade of C.",
      "cid": [],
      "transfer": [
        "CSU"
      ],
      "description": "This course offers a solid foundation in trigonometry essential for studying Calculus. Topics covered include trigonometric functions and their inverses, graphing these functions, identities and proofs related to trigonometric expressions, trigonometric equations, solving right triangles, applying the Law of Cosines and Law of Sines to solve triangles, polar coordinates, and an introduction to vectors.",
      "notes": [],
      "offered": [
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 0,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-108"
        }
      ]
    },
    {
      "code": "MATH-110",
      "subject": "MATH",
      "number": "110",
      "title": "College Mathematics",
      "units": "4",
      "hours": "54 hours lecture; 36 hours activity; 90 hours total",
      "prerequisite": "Completion of Intermediate Algebra level content or equivalent or appropriate placement.",
      "cid": [],
      "transfer": [
        "CSU"
      ],
      "description": "This course covers polynomial, absolute value, radical, rational, exponential, logarithmic, and trigonometric equations, functions and their graphs; analytic geometry and polar coordinates. This course is intended for students interested in the sciences who are not in a major requiring calculus.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 4,
          "open": 3,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-110"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 2,
          "open": 2,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-110"
        }
      ]
    },
    {
      "code": "MATH-115",
      "subject": "MATH",
      "number": "115",
      "title": "Applied Calculus",
      "units": "5",
      "hours": "90 hours lecture; 90 hours total",
      "prerequisite": "Placement as determined by the college's multiple measures assessment process or completion of a course taught at or above the level of college algebra.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course presents a study of the techniques of calculus with emphasis on applications to business, life sciences and social sciences. Topics include modeling, applications of derivatives and integrals for polynomial, rational, exponential and logarithmic functions.",
      "notes": [],
      "offered": [
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 2,
          "open": 2,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-115"
        }
      ]
    },
    {
      "code": "MATH-130",
      "subject": "MATH",
      "number": "130",
      "title": "Mathematical Concepts for Elementary School Teachers-Number Systems",
      "units": "3",
      "hours": "54 hours lecture; 54 hours total",
      "prerequisite": "Completion of Intermediate Algebra level content or equivalent or appropriate placement.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course emphasizes problem solving techniques and mathematical structure associated with numeration, set theory, elementary number theory, the real number system, ratio, proportion and patterns. Designed for prospective elementary teachers, this course includes activity-based explorations implementing the common core state curriculum standards.",
      "notes": [],
      "offered": [
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-130"
        }
      ]
    },
    {
      "code": "MATH-220",
      "subject": "MATH",
      "number": "220",
      "title": "Linear Algebra",
      "units": "3",
      "hours": "54 hours lecture; 54 hours total",
      "prerequisite": "Completion of MATH-C2220 or equivalent with a minimum grade of C.",
      "advisory": "Completion of MATH-221 with a minimum grade of C.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Properties of vectors are investigated in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-220"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-220"
        }
      ]
    },
    {
      "code": "MATH-221",
      "subject": "MATH",
      "number": "221",
      "title": "Multivariable Calculus",
      "units": "5",
      "hours": "90 hours lecture; 90 hours total",
      "prerequisite": "Completion of MATH-C2220 with a minimum grade of C.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "The third semester of a three course sequence in differential and integral calculus. Topics include vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Green's Theorem, Stokes' Theorem, and divergence theorem. Primarily for majors of mathematics, engineering, and science.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 1,
          "open": 0,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-221"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-221"
        }
      ]
    },
    {
      "code": "MATH-222",
      "subject": "MATH",
      "number": "222",
      "title": "Differential Equations",
      "units": "3",
      "hours": "54 hours lecture; 54 hours total",
      "prerequisite": "Completion of MATH-221 with a minimum grade of C.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course is an introduction to ordinary differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. Students are introduced to the theoretical aspects of differential equations, including establishing the existence of solutions, applying a variety of techniques for obtaining solutions, series solutions, and singular points. Laplace transforms and linear systems are also covered.",
      "notes": [],
      "offered": [
        {
          "term": "fall-2026",
          "name": "Fall 2026",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/fall-2026/math/#math-222"
        },
        {
          "term": "spring-2027",
          "name": "Spring 2027",
          "sections": 1,
          "open": 1,
          "url": "/c/napa-valley-college/schedule/spring-2027/math/#math-222"
        }
      ]
    },
    {
      "code": "MATH-235",
      "subject": "MATH",
      "number": "235",
      "title": "Finite Mathematics",
      "units": "3",
      "hours": "54 hours lecture; 54 hours total",
      "prerequisite": "Completion of High School Algebra 2 or Intermediate Algebra level content with a minimum grade of C, or appropriate placement.",
      "cid": [],
      "transfer": [
        "UC",
        "CSU"
      ],
      "description": "This course covers linear functions, systems of linear equations and inequalities, matrices, linear programming, mathematics of finance, sets and Venn diagrams, combinatorial techniques and an introduction to probability. Applications from business, economics and social sciences are included in this class.",
      "notes": [],
      "offered": []
    }
  ]
}