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Exercises DataBase
for the first year class in Mathematics
in Scuola Normale Superiore

Andrea C. G. Mennucci
(version April 28, 2024)
Pisa, Italy

Collections of exercises and theoretical bits proposed to first year students in “Scuola Normale Superiore”.

[this is a draft there are many errors]

1 Introduction

[100]

2 Notations

[002_notazioni]

3 Fundamentals

[003_fondamenti]

4 Natural numbers

[003_numeri]

5 Groups, Rings, Fields

[1ZD]

6 Real line

[004_retta-reale]

7 Sequences and series

[005_successioni-e-serie]

8 Topology

[006_topologia]

9 Miscellanea

[2FB]

10 Metric spaces

[007_spazi-metrici]

11 Dimension

[008_dimensione]

12 Normed spaces

[009_spazi-normati]

13 Semicontinuity, right and left limits

[00B_semi-continuita-limiti-destri-e-sinistri]

14 Continuity

[00C_continuita]

15 Convex functions and sets

[00D_funzioni-e-insiemi-convessi]

16 Riemann integral

[00F_integrale-di-riemann]

17 Differentiable functions

[00G_funzioni-derivabili]

18 Limits of functions

[00H_limiti-di-funzioni]

19 Power series

[00J_serie-di-potenze]

20 Analytic functions

[00K_analitiche]

21 Curve

[00M_curve]

22 Surfaces

[00P_superfici]

23 Ordinary Differential equations

[00Q_equazioni-differenziali]

24 Written exams and pseudo–exams

[00R_pseudocompitini]

Ideas and exercises without solution

[00S_idee-e-esercizi-senza-soluzione]



Bibliography

[1VV][1VT]


[2B1]

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