MATH172

INTRODUCTION TO REAL ANALYSIS

This course is offered in a current or upcoming term. Check the official course schedule before registering.
Also listed under 3 other titles
  • INTRODUCTION TO ANALYSIS
  • Introduction to Modern Analysis
  • INTRO TO ANALYSIS
Department
Mathematics
Terms offered
32
Data refreshed
Sep 29, 2026

Description

Real analysis provides a language and unifying framework for theories encountered throughout mathematics. In this course, students learn to understand, formulate and prove mathematical statements. Ideas first encountered in calculus-convergence, completeness and integration-are studied in depth. Other topics include metric spaces, normed spaces, compactness and measure theory (Lebesgue integration). Required for mathematics majors by the junior year, and earlier if possible.

Syllabi

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Offering history & forecast 2016–2026

1995
2026
Sections offered by academic year and season, with estimated offering chances for future years above the divider
YearFallSpringSummerIntersession
2030 2030 Fall: 56% chance, medium confidence. Offered in every fall term since 2018. Department course count falling about 6% per year. 2030 Spring: 7% chance, medium confidence. Offered in 0 of 9 spring terms since 2018. 2030 Summer: 7% chance, medium confidence. Offered in 0 of 9 summer terms since 2018. 2030 Intersession: 8% chance, medium confidence. Offered in 0 of 6 intersession terms since 2020.
2029 2029 Fall: 61% chance, medium confidence. Offered in every fall term since 2017. Department course count falling about 6% per year. 2029 Spring: 6% chance, medium confidence. Offered in 0 of 10 spring terms since 2017. 2029 Summer: 6% chance, medium confidence. Offered in 0 of 10 summer terms since 2017. 2029 Intersession: 7% chance, medium confidence. Offered in 0 of 7 intersession terms since 2017.
2028 2028 Fall: 65% chance, medium confidence. Offered in every fall term since 2016. Department course count falling about 4% per year. 2028 Spring: 5% chance, medium confidence. Offered in 0 of 11 spring terms since 2016. 2028 Summer: 5% chance, medium confidence. Offered in 0 of 11 summer terms since 2016. 2028 Intersession: 7% chance, medium confidence. Offered in 0 of 7 intersession terms since 2017.
2027 2027 Fall: 69% chance, medium confidence. Offered in every fall term since 2015. Department course count falling about 3% per year. 2027 Spring: 5% chance, high confidence. Offered in 0 of 12 spring terms since 2015. 2027 Summer: 5% chance, high confidence. Offered in 0 of 12 summer terms since 2015. 2027 Intersession: 6% chance, medium confidence. Offered in 0 of 7 intersession terms since 2017.
2026 1 section Not offered Not offered No data for this term
2025 1 section Not offered Not offered Not offered
2024 1 section Not offered Not offered Not offered
2023 1 section Not offered Not offered Not offered
2022 1 section Not offered Not offered Not offered
2021 1 section Not offered Not offered Not offered
2020 1 section Not offered Not offered Not offered
2019 1 section Not offered Not offered No data for this term
2018 1 section Not offered Not offered No data for this term
2017 1 section Not offered Not offered Not offered
2016 1 section Not offered Not offered No data for this term
Forecast Under 15% 15–39% 40–69% 70–89% 90%+ Not enough history
Fall Spring Summer Intersession Darker means more sections Not offered No data for term

Future estimates combine recent offering frequency with detected multi-year cycles. Hover a cell for confidence and evidence; low-confidence estimates are marked with ~.

Meeting times

Most recent first
  • Tue, Thu, 10:25 AM–11:40 AM BP316 202620091999
  • Mon, Wed, 12:00 PM–1:15 PM BP316 2025
  • Mon, Wed, 4:15 PM–5:30 PM Sackler Science Center S122 2019
  • Tue, Thu, 9:00 AM–10:15 AM BP316 2017
  • Mon, Thu, 1:25 PM–2:40 PM BP316 201220112003
  • Tue, Thu, 4:15 PM–5:30 PM BP326 201020082007
  • Tue, Fri, 2:50 PM–4:05 PM BP220 2006
  • Tue, Fri, 12:00 PM–1:15 PM BP220 2005
2026–27 1 entry
Credit-bearing sections of MATH172, 2026–27
TermProfessorTypeCreditsEnrollmentCRN
Fall 2026Amir Babak AazamiLecture1 8 of 25 enrolled20031
2025–26 1 entry
Credit-bearing sections of MATH172, 2025–26
TermProfessorTypeCreditsEnrollmentCRN
Fall 2025Ali MaalaouiLecture1 18 of 25 enrolled20031
2024–25 1 entry
Credit-bearing sections of MATH172, 2024–25
TermProfessorTypeCreditsEnrollmentCRN
Fall 2024Ali MaalaouiLecture1 14 of 25 enrolled20031
2023–24 1 entry
Credit-bearing sections of MATH172, 2023–24
TermProfessorTypeCreditsEnrollmentCRN
Fall 2023Ali MaalaouiLecture1 10 of 25 enrolled20031
2022–23 1 entry
Credit-bearing sections of MATH172, 2022–23
TermProfessorTypeCreditsEnrollmentCRN
Fall 2022Ali MaalaouiLecture1 7 of 25 enrolled20031
2021–22 1 entry
Credit-bearing sections of MATH172, 2021–22
TermProfessorTypeCreditsEnrollmentCRN
Fall 2021Aghil Alaee KhanghaLecture1 10 of 25 enrolled20168
2020–21 1 entry
Credit-bearing sections of MATH172, 2020–21
TermProfessorTypeCreditsEnrollmentCRN
Fall 2020Aghil Alaee KhanghaLecture1 12 of 25 enrolled20168
2019–20 1 entry
Credit-bearing sections of MATH172, 2019–20
TermProfessorTypeCreditsEnrollmentCRN
Fall 2019Amir Babak AazamiLecture1 36 of 24 enrolled20168
2018–19 1 entry
Credit-bearing sections of MATH172, 2018–19
TermProfessorTypeCreditsEnrollmentCRN
Fall 2018Natalia C. SternbergLecture1 12 of 24 enrolled20168
2017–18 1 entry
Credit-bearing sections of MATH172, 2017–18
TermProfessorTypeCreditsEnrollmentCRN
Fall 2017Natalia C. SternbergLecture1 26 of 24 enrolled20168
2016–17 1 entry
Credit-bearing sections of MATH172, 2016–17
TermProfessorTypeCreditsEnrollmentCRN
Fall 2016Gideon Bahir-MaschlerLecture1 22 of 24 enrolled20168
2015–16 1 entry
Credit-bearing sections of MATH172, 2015–16
TermProfessorTypeCreditsEnrollmentCRN
Fall 2015Natalia C. SternbergLecture1 21 of 24 enrolled20168
2014–15 1 entry
Credit-bearing sections of MATH172, 2014–15
TermProfessorTypeCreditsEnrollmentCRN
Fall 2014Lawrence E. MorrisLecture1 12 of 24 enrolled20168
2013–14 1 entry
Credit-bearing sections of MATH172, 2013–14
TermProfessorTypeCreditsEnrollmentCRN
Fall 2013Lawrence E. MorrisLecture1 21 of 25 enrolled20168
2012–13 1 entry
Credit-bearing sections of MATH172, 2012–13
TermProfessorTypeCreditsEnrollmentCRN
Fall 2012Natalia C. SternbergLecture1 26 of 25 enrolled20168
2011–12 1 entry
Credit-bearing sections of MATH172, 2011–12
TermProfessorTypeCreditsEnrollmentCRN
Fall 2011Natalia C. SternbergLecture1 20 of 25 enrolled20168
2010–11 1 entry
Credit-bearing sections of MATH172, 2010–11
TermProfessorTypeCreditsEnrollmentCRN
Fall 2010Gideon Bahir-MaschlerLecture1 16 of 20 enrolled27180
2009–10 1 entry
Credit-bearing sections of MATH172, 2009–10
TermProfessorTypeCreditsEnrollmentCRN
Fall 2009David E. JoyceLecture1 17 of 20 enrolled20095
2008–09 1 entry
Credit-bearing sections of MATH172, 2008–09
TermProfessorTypeCreditsEnrollmentCRN
Fall 2008Gideon Bahir-MaschlerLecture1 19 of 20 enrolled20095
2007–08 1 entry
Credit-bearing sections of MATH172, 2007–08
TermProfessorTypeCreditsEnrollmentCRN
Fall 2007Arthur W. ChouLecture1 14 of 25 enrolled20095
2006–07 1 entry
Credit-bearing sections of MATH172, 2006–07
TermProfessorTypeCreditsEnrollmentCRN
Fall 2006Lawrence E. MorrisLecture1 10 of 25 enrolled20095
2005–06 1 entry
Credit-bearing sections of MATH172, 2005–06
TermProfessorTypeCreditsEnrollmentCRN
Fall 2005Natalia C. SternbergLecture1 24 of 25 enrolled20095
2004–05 1 entry
Credit-bearing sections of MATH172, 2004–05
TermProfessorTypeCreditsEnrollmentCRN
Fall 2004Natalia C. SternbergLecture1 16 of 25 enrolled20095
2003–04 1 entry
Credit-bearing sections of MATH172, 2003–04
TermProfessorTypeCreditsEnrollmentCRN
Fall 2003Arthur W. ChouLecture1 5 of 25 enrolled20095
2002–03 1 entry
Credit-bearing sections of MATH172, 2002–03
TermProfessorTypeCreditsEnrollmentCRN
Fall 2002Natalia C. SternbergLecture1 9 of 25 enrolled20321
2001–02 1 entry
Credit-bearing sections of MATH172, 2001–02
TermProfessorTypeCreditsEnrollmentCRN
Fall 2001Lawrence E. MorrisLecture1 12 of 30 enrolled20321
2000–01 1 entry
Credit-bearing sections of MATH172, 2000–01
TermProfessorTypeCreditsEnrollmentCRN
Fall 2000Natalia C. SternbergLecture1 11 of 30 enrolled20321
1999–00 1 entry
Credit-bearing sections of MATH172, 1999–00
TermProfessorTypeCreditsEnrollmentCRN
Fall 1999Natalia C. SternbergLecture1 5 of 35 enrolled20321
1998–99 1 entry
Credit-bearing sections of MATH172, 1998–99
TermProfessorTypeCreditsEnrollmentCRN
Fall 1998Natalia C. SternbergLecture1 11 of 35 enrolled20321
1997–98 1 entry
Credit-bearing sections of MATH172, 1997–98
TermProfessorTypeCreditsEnrollmentCRN
Fall 1997Natalia C. SternbergLecture1 14 of 35 enrolled20321
1996–97 1 entry
Credit-bearing sections of MATH172, 1996–97
TermProfessorTypeCreditsEnrollmentCRN
Fall 1996Natalia C. SternbergLecture1 12 of 35 enrolled20321
1995–96 1 entry
Credit-bearing sections of MATH172, 1995–96
TermProfessorTypeCreditsEnrollmentCRN
Fall 1995Natalia C. SternbergLecture1 7 of 35 enrolled20321