Challenge 3: A Makefile for the Project, and What Running make Twice Does — Possible Solution
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Makefile:

program: main.o math_utils.o
	gcc main.o math_utils.o -o program

main.o: main.c math_utils.h
	gcc -c main.c -o main.o

math_utils.o: math_utils.c math_utils.h
	gcc -c math_utils.c -o math_utils.o

clean:
	rm -f *.o program

(Note: the indented lines under each target must use a literal TAB
character, not spaces -- a real, common Makefile gotcha in its own
right.)

Running `make` the FIRST time: none of the target files (program,
main.o, math_utils.o) exist yet, so every rule's dependencies are
"newer" than a nonexistent target by definition. make runs every
compile and link command: compiles main.c to main.o, compiles
math_utils.c to math_utils.o, then links both into program.

Running `make` a SECOND time, with NOTHING changed in between: make
checks each target's modification timestamp against its listed
dependencies. main.o now exists and is newer than main.c and
math_utils.h (nothing edited them since main.o was built) -- so
main.o's rule is considered up to date and its recompile command does
NOT run. The same reasoning applies to math_utils.o, and then to
program itself (both math_utils.o and main.o remain unchanged, so
program's own link step also doesn't re-run). make prints something
like "make: 'program' is up to date." and exits without recompiling or
re-linking anything at all.

WHY THIS WORKS AS AN ANSWER
------------------------------
This correctly follows the chapter's own dependency-rule pattern
(listing math_utils.h as a dependency of both .o files, not just the
corresponding .c file), and explains the SECOND make invocation
correctly as doing genuinely nothing -- not "rebuilding everything
again" -- because every target's timestamp is already newer than its
dependencies, which is precisely the incremental-rebuild behavior the
chapter names as make's whole reason for existing.